{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T03:05:44Z","timestamp":1777777544030,"version":"3.51.4"},"reference-count":126,"publisher":"Emerald","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,8,19]]},"abstract":"<jats:p>Resilience has come to mean several things in the system sciences. The term is used to describe systems whose function is robust with respect to external disturbances. It is used to describe systems that tolerate faults in some internal component. It is also used to describe systems that have the capacity to recover after a complete collapse of system function. This monograph defines resilience in the last sense. This notion of resilience is often called ecological resilience. For a system to be ecologically resilient, one first accepts system collapse as being inevitable and then requires that the resources for subsequent system recovery be buried in the wreckage of that collapse.<\/jats:p>\n                  <jats:p>The ecological concept of a regime shift plays an important role in describing abrupt shifts in ecosystem behavior. In particular, the collapse of system function may be seen as an instance of a regime shift. Restoring a collapsed ecosystem often involves walking the system through a sequence of alternative states before full recovery can be achieved. The transitions between these alternative states are also regime shifts. But in this case, these regime shifts are purposefully triggered to speed up the recovery process. Managing regime shifts that trigger system collapse provides a way to conserve existing system function. Managing regime shifts that systematically rebuild lost system function provides a way to restore lost system function. Regime shifts, therefore, play an important role in enhancing the ecological resilience of a dynamical system.<\/jats:p>\n                  <jats:p>This monograph formalizes the ecologist\u2019s regime shift concept by identifying regimes with components (also known as basic sets) of a Morse decomposition of the system\u2019s chain recurrent set. This formalization allows the identification of two distinct regime shift mechanisms; one triggered by external shocks (shock-induced regime shift) and the other triggered by bifurcations of the system flow (bifurcation-induced regime shift). This allows one to define ecological resilience in terms of a discrete abstraction (called the regime transition system) that characterizes the sequences of shock-induced regime shifts that can be triggered in the system. This monograph shows how that transition system can be constructed from the system\u2019s differential equation model and demonstrates how it can be used to enhance the resilience of ecosystem foodwebs through the careful management of the system\u2019s regime shifts.<\/jats:p>","DOI":"10.1561\/2600000021","type":"journal-article","created":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T09:57:47Z","timestamp":1597831067000},"page":"384-499","source":"Crossref","is-referenced-by-count":0,"title":["Achieving Ecological Resilience Through Regime Shift Management"],"prefix":"10.1108","volume":"7","author":[{"given":"M. D.","family":"Lemmon","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Notre Dame ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2020,8,19]]},"reference":[{"issue":"1-3","key":"2026033114235336700_ref001","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01587095","article-title":"An implementation of Karmarkar\u2019s algorithm for linear programming","volume":"44","author":"Adler","year":"1989","journal-title":"Mathematical Programming"},{"key":"2026033114235336700_ref002","first-page":"366","volume-title":"Hybrid Systems","author":"Antsaklis","year":"1992"},{"issue":"1","key":"2026033114235336700_ref003","first-page":"161","article-title":"Cyber-physical systems","volume":"12","author":"Baheti","year":"2011","journal-title":"The Impact of Control Technology"},{"key":"2026033114235336700_ref004","article-title":"A new method for improvement of robustness bounds for linear state equations","author":"Barmish","year":"1986","journal-title":"Proceedings of the Princeton Conference on Information Sciences and Systems"},{"key":"2026033114235336700_ref005","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-62006-5","volume-title":"Stability Theory of Dynamical Systms","author":"Bhatia","year":"1970"},{"issue":"3","key":"2026033114235336700_ref006","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1073\/pnas.0811729106","article-title":"Turning back from the brink: Detecting an impending regime shift in time to avert it","volume":"106","author":"Biggs","year":"2009","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026033114235336700_ref007","volume-title":"Diagnosis and Fault-Tolerant Control","author":"Blanke","year":"2006"},{"issue":"2","key":"2026033114235336700_ref008","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/87.556026","article-title":"Multivariable adaptive algorithms for reconfigurable flight control","volume":"5","author":"Bodson","year":"1997","journal-title":"IEEE Transactions on Control Systems Technology"},{"issue":"6","key":"2026033114235336700_ref009","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1111\/j.1461-0248.2012.01777.x","article-title":"Mechanistic theory and modelling of complex food-web dynamics in lake constance","volume":"15","author":"Boit","year":"2012","journal-title":"Ecology Letters"},{"key":"2026033114235336700_ref010","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","volume-title":"Linear Matrix Inequalities in System and Control Theory","author":"Boyd","year":"1994"},{"issue":"7","key":"2026033114235336700_ref011","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1890\/03-9000","article-title":"Toward a metabolic theory of ecology","volume":"85","author":"Brown","year":"2004","journal-title":"Ecology"},{"issue":"6033","key":"2026033114235336700_ref012","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1126\/science.1203672","article-title":"Early warnings of regime shifts: A whole-ecosystem experiment","volume":"332","author":"Carpenter","year":"2011","journal-title":"Science"},{"issue":"3","key":"2026033114235336700_ref013","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1890\/1051-0761(1999)009[0751:MOEFLS]2.0.CO;2","article-title":"Management of eutrophication for lakes subject to potentially irreversible change","volume":"9","author":"Carpenter","year":"1999","journal-title":"Ecological Applications"},{"key":"2026033114235336700_ref014","doi-asserted-by":"crossref","DOI":"10.1002\/9780470142622.ch1","volume-title":"Stability of Complex Reaction Networks","author":"Clarke","year":"1980"},{"key":"2026033114235336700_ref015","doi-asserted-by":"crossref","DOI":"10.1090\/cbms\/038","volume-title":"Isolated Invariant Sets and the Morse Index","author":"Conley","year":"1978"},{"issue":"49","key":"2026033114235336700_ref016","doi-asserted-by":"crossref","first-page":"19175","DOI":"10.1073\/pnas.0705731104","article-title":"Subnetwork analysis reveals dynamic features of complex (bio) chemical networks","volume":"104","author":"Conradi","year":"2007","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026033114235336700_ref017","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1038\/387253a0","article-title":"The value of the world\u2019s ecosystem services and natural capital","volume":"387","author":"Costanza","year":"1997","journal-title":"Nature"},{"key":"2026033114235336700_ref018","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2181-2","volume-title":"Ideals, Varieties, and Algorithms","author":"Cox","year":"1992"},{"issue":"38","key":"2026033114235336700_ref019","doi-asserted-by":"crossref","first-page":"14308","DOI":"10.1073\/pnas.0802430105","article-title":"Slowing down as an early warning signal for abrupt climate change","volume":"105","author":"Dakos","year":"2008","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026033114235336700_ref020","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3354\/meps225053","article-title":"Overfishing drives a trophic cascade in the black sea","volume":"225","author":"Daskalov","year":"2002","journal-title":"Marine Ecology Progress Series"},{"issue":"25","key":"2026033114235336700_ref021","doi-asserted-by":"crossref","first-page":"10518","DOI":"10.1073\/pnas.0701100104","article-title":"Trophic cascades triggered by overfishing reveal possible mechanisms of ecosystem regime shifts","volume":"104","author":"Daskalov","year":"2007","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026033114235336700_ref022","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-2342-6","volume-title":"Dynamics of Nutrient Cycling and Food Webs.","author":"DeAngelis","year":"1992"},{"key":"2026033114235336700_ref023","volume-title":"Computing in Algebraic Geometry: A Quick Start Using SINGULAR","author":"Decker","year":"2006"},{"issue":"1-5","key":"2026033114235336700_ref024","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0277-3791(99)00081-5","article-title":"Abrupt onset and termination of the african humid period: Rapid climate responses to gradual insolation forcing","volume":"19","author":"Demenocal","year":"2000","journal-title":"Quaternary Science Reviews"},{"issue":"5891","key":"2026033114235336700_ref025","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1126\/science.1156401","article-title":"Spreading dead zones and consequences for marine ecosystems","volume":"321","author":"Diaz","year":"2008","journal-title":"Science"},{"key":"2026033114235336700_ref026","first-page":"49","volume-title":"Bifurcation Control","author":"Dobson","year":"2003"},{"issue":"3","key":"2026033114235336700_ref027","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1109\/59.260912","article-title":"New methods for computing a closest saddle node bifurcation and worst case load power margin for voltage collapse","volume":"8","author":"Dobson","year":"1993","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033114235336700_ref028","first-page":"265","article-title":"AUTO: A program for the automatic bifurcation analysis of autonomous systems","volume":"30","author":"Doedel","year":"1981","journal-title":"Congressus Numerantium"},{"key":"2026033114235336700_ref029","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/978-3-0348-5681-2_10","volume-title":"Continuation Techniques and Bifurcation Problems","author":"Doedel","year":"1990"},{"issue":"1","key":"2026033114235336700_ref030","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s12080-008-0027-z","article-title":"Using mean first passage times to quantify equilibrium resilience in perturbed intraguild predation systems","volume":"2","author":"Drury","year":"2009","journal-title":"Theoretical Ecology"},{"key":"2026033114235336700_ref031","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195085457.001.0001","volume-title":"Geometric Methods for Discrete Dynamical Systems","author":"Easton","year":"1998"},{"key":"2026033114235336700_ref032","volume-title":"Computational Topology: An Introduction","author":"Edelsbrunner","year":"2010"},{"key":"2026033114235336700_ref033","article-title":"Stabilator Reconfiguration Flight Testing on the F\/A-18E\/F","author":"Egbert","year":"2001","journal-title":"Proceedings of the SAE Control and Guidance Meeting."},{"issue":"6","key":"2026033114235336700_ref034","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1007\/s10021-002-0227-0","article-title":"Regime shifts in the sahara and sahel: Interactions between ecological and climatic systems in Northern Africa","volume":"6","author":"Foley","year":"2003","journal-title":"Ecosystems"},{"issue":"3","key":"2026033114235336700_ref035","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.gloenvcha.2006.04.002","article-title":"Resilience: The emergence of a perspective for social\u2013 ecological systems analyses","volume":"16","author":"Folke","year":"2006","journal-title":"Global Environmental Change"},{"key":"2026033114235336700_ref036","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1146\/annurev.ecolsys.35.021103.105711","article-title":"Regime shifts, resilience, and biodiversity in ecosystem management","volume":"35","author":"Folke","year":"2004","journal-title":"Annual Review of Ecology, Evolution, and Systematics"},{"issue":"6","key":"2026033114235336700_ref037","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1137\/S106482750238911X","article-title":"Detecting and locating nearoptimal almost-invariant sets and cycles","volume":"24","author":"Froyland","year":"2003","journal-title":"SIAM Journal on Scientific Computing"},{"issue":"5495","key":"2026033114235336700_ref038","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1126\/science.290.5495.1358","article-title":"Crossing the Hopf bifurcation in a live predator-prey system","volume":"290","author":"Fussmann","year":"2000","journal-title":"Science"},{"issue":"1","key":"2026033114235336700_ref039","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-5-175","article-title":"Computation of elementary modes: A unifying framework and the new binary approach","volume":"5","author":"Gagneur","year":"2004","journal-title":"BMC Bioinformatics"},{"key":"2026033114235336700_ref040","first-page":"2038","article-title":"The LMI control toolbox","volume":"2","author":"Gahinet","year":"1994","journal-title":"IEEE Conference on Decision and Control"},{"issue":"3","key":"2026033114235336700_ref041","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/9.486646","article-title":"Affine parameterdependent Lyapunov functions and real parametric uncertainty","volume":"41","author":"Gahinet","year":"1996","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"2026033114235336700_ref042","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/S0273-0979-07-01191-3","article-title":"Barcodes: The persistent topology of data","volume":"45","author":"Ghrist","year":"2008","journal-title":"Bulletin of the American Mathematical Society"},{"key":"2026033114235336700_ref043","first-page":"227","article-title":"SINGULAR\u2014A computer algebra system for polynomial computations","author":"Greuel","year":"2001","journal-title":"Symbolic Computation and Automated Reasoning"},{"issue":"1","key":"2026033114235336700_ref044","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10021-003-0142-z","article-title":"Ecological thresholds: The key to successful environmental management or an important concept with no practical application?","volume":"9","author":"Groffman","year":"2006","journal-title":"Ecosystems"},{"key":"2026033114235336700_ref045","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-57318-6","volume-title":"Hybrid Systems","author":"Grossman","year":"1993"},{"key":"2026033114235336700_ref046","volume-title":"Panarchy: Understanding Transformations in Human and Natural Systems","author":"Gunderson","year":"2001"},{"key":"2026033114235336700_ref047","doi-asserted-by":"crossref","DOI":"10.1515\/9781400832248","volume-title":"Nonnegative and Compartmental Dynamical Systems","author":"Haddad","year":"2010"},{"issue":"1","key":"2026033114235336700_ref048","doi-asserted-by":"crossref","first-page":"49","DOI":"10.5268\/IW-5.1.566","article-title":"A global lake ecological observatory network (GLEON) for synthesising high-frequency sensor data for validation of deterministic ecological models","volume":"5","author":"Hamilton","year":"2015","journal-title":"Inland Waters"},{"key":"2026033114235336700_ref049","first-page":"363","article-title":"On the inverse problem of reaction kinetics","volume":"30","author":"H\u00e1rs","year":"1981","journal-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai (Szeged, Hungary, 1979) Qualitative Theory of Differential Equations (M. Farkas ed.)."},{"key":"2026033114235336700_ref050","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719222","volume-title":"Ordinary Differential Equations","author":"Hartman","year":"2002","edition":"2nd"},{"issue":"3","key":"2026033114235336700_ref051","doi-asserted-by":"crossref","first-page":"896","DOI":"10.2307\/1940591","article-title":"Chaos in a three-species food chain","volume":"72","author":"Hastings","year":"1991","journal-title":"Ecology"},{"key":"2026033114235336700_ref052","volume-title":"Algebraic Topology","author":"Hatcher","year":"2002"},{"key":"2026033114235336700_ref053","volume-title":"New Models for Ecosystem Dynamics and Restoration","author":"Hobbs","year":"2009"},{"issue":"2","key":"2026033114235336700_ref054","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1526-100X.1996.tb00112.x","article-title":"Towards a conceptual framework for restoration ecology","volume":"4","author":"Hobbs","year":"1996","journal-title":"Restoration Ecology"},{"key":"2026033114235336700_ref055","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev.es.04.110173.000245","article-title":"Resilience and stability of ecological systems","volume":"4","author":"Holling","year":"1973","journal-title":"Annual Review of Ecology and Systematics"},{"key":"2026033114235336700_ref056","first-page":"31","volume-title":"Engineering within Ecological Constraints","author":"Holling","year":"1996"},{"issue":"5","key":"2026033114235336700_ref057","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/s10021-001-0101-5","article-title":"Understanding the complexity of economic, ecological, and social systems","volume":"4","author":"Holling","year":"2001","journal-title":"Ecosystems"},{"issue":"5178","key":"2026033114235336700_ref058","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1126\/science.265.5178.1547","article-title":"Catastrophes, phase shifts, and large-scale degradation of a caribbean coral reef","volume":"265","author":"Hughes","year":"1994","journal-title":"Science"},{"issue":"4","key":"2026033114235336700_ref059","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.cub.2006.12.049","article-title":"Phase shifts, herbivory, and the resilience of coral reefs to climate change","volume":"17","author":"Hughes","year":"2007","journal-title":"Current Biology"},{"issue":"4","key":"2026033114235336700_ref060","doi-asserted-by":"crossref","first-page":"218","DOI":"10.9746\/jcmsi.5.218","article-title":"Sum of squares based input-to-state stability analysis of polynomial nonlinear systems","volume":"5","author":"Ichihara","year":"2012","journal-title":"SICE Journal of Control, Measurement, and System Integration"},{"key":"2026033114235336700_ref061","doi-asserted-by":"crossref","DOI":"10.1142\/4681","volume":"17","author":"Irwin","year":"2001","journal-title":"Smooth Dynamical Systems"},{"issue":"1","key":"2026033114235336700_ref062","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.arcontrol.2008.01.001","article-title":"Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection","volume":"32","author":"Isidori","year":"2008","journal-title":"Annual Reviews in Control"},{"key":"2026033114235336700_ref063","volume-title":"Compartmental Analysis in Biology and Medicine","author":"Jacquez","year":"1972"},{"issue":"1","key":"2026033114235336700_ref064","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1137\/1035003","article-title":"Qualitative theory of compartmental systems","volume":"35","author":"Jacquez","year":"1993","journal-title":"SIAM Review"},{"issue":"5","key":"2026033114235336700_ref065","doi-asserted-by":"crossref","first-page":"e5653","DOI":"10.1371\/journal.pone.0005653","article-title":"Rapid recovery of damaged ecosystems","volume":"4","author":"Jones","year":"2009","journal-title":"PloS One"},{"key":"2026033114235336700_ref066","volume-title":"Computational Homology","author":"Kaczynski","year":"2006"},{"issue":"4","key":"2026033114235336700_ref067","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s10208-004-0163-9","article-title":"An algorithmic approach to chain recurrence","volume":"5","author":"Kalies","year":"2005","journal-title":"Foundations of Computational Mathematics"},{"issue":"4","key":"2026033114235336700_ref068","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1049\/ip-syb:20050035","article-title":"Algorithmic approaches for computing elementary modes in large biochemical reaction networks","volume":"152","author":"Klamt","year":"2005","journal-title":"IEE Proceedings-Systems Biology"},{"issue":"7","key":"2026033114235336700_ref069","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1109\/5.871307","article-title":"Supervisory control of hybrid systems","volume":"88","author":"Koutsoukos","year":"2000","journal-title":"Proceedings of the IEEE"},{"key":"2026033114235336700_ref070","volume-title":"Modeling and Control of Logical Discrete Event Systems","author":"Kumar","year":"2012"},{"issue":"2","key":"2026033114235336700_ref071","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1109\/TAC.1966.1098315","article-title":"Finite time stochastic stability and the analysis of tracking systems","volume":"11","author":"Kushner","year":"1966","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114235336700_ref072","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BFb0064937","volume-title":"Stability of Stochastic Dynamical Systems","author":"Kushner","year":"1972"},{"key":"2026033114235336700_ref073","volume-title":"Elements of Applied Bifurcation Theory","author":"Kuznetsov","year":"2013"},{"issue":"27","key":"2026033114235336700_ref074","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.ifacol.2015.11.174","article-title":"Using elementary flux modes to estimate the distance to regime shifts in kinetic systems","volume":"48","author":"Lemmon","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"2026033114235336700_ref075","first-page":"284","volume-title":"IEEE International Symposium on Computer Aided Control Systems Design","author":"Lofberg","year":"2004"},{"key":"2026033114235336700_ref076","first-page":"3880","volume-title":"IEEE Conference on Decision and Control","author":"Madeira","year":"2016"},{"issue":"1","key":"2026033114235336700_ref077","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ecolmodel.2005.11.011","article-title":"Fisher information and dynamic regime changes in ecological systems","volume":"195","author":"Mayer","year":"2006","journal-title":"Ecological Modelling"},{"key":"2026033114235336700_ref078","doi-asserted-by":"crossref","DOI":"10.1515\/9781400881802","volume-title":"Morse Theory","author":"Milnor","year":"1963"},{"key":"2026033114235336700_ref079","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BFb0095240","volume-title":"Dynamical Systems","author":"Mischaikow","year":"1995"},{"key":"2026033114235336700_ref080","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1017\/S0962492902000065","article-title":"Topological techniques for efficient rigorous computation in dynamics","volume":"11","author":"Mischaikow","year":"2002","journal-title":"Acta Numerica"},{"issue":"4","key":"2026033114235336700_ref081","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF01200146","article-title":"On decomposing systems of polynomial equations with finitely many solutions","volume":"4","author":"M\u00f6ller","year":"1993","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"issue":"10","key":"2026033114235336700_ref082","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/S0169-5347(00)01948-0","article-title":"Coral reef disturbance and resilience in a human-dominated environment","volume":"15","author":"Nystr\u00f6m","year":"2000","journal-title":"Trends in Ecology & Evolution"},{"key":"2026033114235336700_ref083","volume-title":"Applied Stochastic Control of Jump Diffusions","author":"\u00d8ksendal","year":"2005"},{"key":"2026033114235336700_ref084","first-page":"223","article-title":"Structural stability theorems","author":"Palis","year":"1970","journal-title":"Global Analysis (Proceedings of Symposia in Pure Mathematics, Vol. XIV, Berkeley, CA, 1968)"},{"key":"2026033114235336700_ref085","first-page":"3482","volume-title":"IEEE Conference on Decision and Control","author":"Papachristodoulou","year":"2002"},{"key":"2026033114235336700_ref086","author":"Parrilo","year":"2000"},{"issue":"3","key":"2026033114235336700_ref087","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1006\/jmsc.2000.0726","article-title":"Ecopath, ecosim, and ecospace as tools for evaluating ecosystem impact of fisheries","volume":"57","author":"Pauly","year":"2000","journal-title":"ICES Journal of Marine Science"},{"issue":"11","key":"2026033114235336700_ref088","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/21.467710","article-title":"Automated fault detection and accommodation: A learning systems approach","volume":"25","author":"Polycarpou","year":"1995","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics"},{"issue":"8","key":"2026033114235336700_ref089","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1109\/TAC.2007.902736","article-title":"A framework for worst-case and stochastic safety verification using barrier certificates","volume":"52","author":"Prajna","year":"2007","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114235336700_ref090","first-page":"741","volume-title":"Proceedings of the 41st IEEE Conference on Decision and Control","author":"Prajna","year":"2002"},{"key":"2026033114235336700_ref091","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10061-5","volume-title":"Stochastic Integration and Differential Equations","author":"Protter","year":"2005"},{"issue":"3","key":"2026033114235336700_ref092","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1512\/iumj.1993.42.42045","article-title":"Positive polynomials on compact semi-algebraic sets","volume":"42","author":"Putinar","year":"1993","journal-title":"Indiana University Mathematics Journal"},{"issue":"1","key":"2026033114235336700_ref093","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1137\/0325013","article-title":"Supervisory control of a class of discrete event processes","volume":"25","author":"Ramadge","year":"1987","journal-title":"SIAM Journal on Control and Optimization"},{"key":"2026033114235336700_ref094","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/978-3-642-93360-8_26","volume-title":"Mathematical Topics in Population Biology, Morphogenesis and Neurosciences","author":"Rinzel","year":"1987"},{"issue":"895","key":"2026033114235336700_ref095","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1086\/282272","article-title":"Graphical representation and stability conditions of predator-prey interactions","volume":"97","author":"Rosenzweig","year":"1963","journal-title":"The American Naturalist"},{"key":"2026033114235336700_ref096","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-3154-0","volume-title":"Ecology of Shallow Lakes","author":"Scheffer","year":"2004"},{"issue":"7260","key":"2026033114235336700_ref097","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1038\/nature08227","article-title":"Early-warning signals for critical transitions","volume":"461","author":"Scheffer","year":"2009","journal-title":"Nature"},{"issue":"12","key":"2026033114235336700_ref098","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.tree.2003.09.002","article-title":"Catastrophic regime shifts in ecosystems: Linking theory to observation","volume":"18","author":"Scheffer","year":"2003","journal-title":"Trends in Ecology & Evolution"},{"issue":"6856","key":"2026033114235336700_ref099","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1038\/35098000","article-title":"Catastrophic shifts in ecosystems","volume":"413","author":"Scheffer","year":"2001","journal-title":"Nature"},{"issue":"8","key":"2026033114235336700_ref100","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0169-5347(93)90254-M","article-title":"Alternative equilibria in shallow lakes","volume":"8","author":"Scheffer","year":"1993","journal-title":"Trends in Ecology & Evolution"},{"issue":"02","key":"2026033114235336700_ref101","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1142\/S0218339094000131","article-title":"On elementary flux modes in biochemical reaction systems at steady state","volume":"2","author":"Schuster","year":"1994","journal-title":"Journal of Biological Systems"},{"key":"2026033114235336700_ref102","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s10021-012-9542-2","article-title":"Conditional heteroskedasticity forecasts regime shift in a whole ecosystem experiment","volume":"15","author":"Seekell","year":"2012","journal-title":"Ecosystems"},{"issue":"8","key":"2026033114235336700_ref103","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1109\/34.868688","article-title":"Normalized cuts and image segmentation","volume":"22","author":"Shi","year":"2000","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026033114235336700_ref104","doi-asserted-by":"crossref","DOI":"10.1002\/9781119968535","volume-title":"Metabolic ecology: A Scaling Approach","author":"Sibly","year":"2012"},{"issue":"1","key":"2026033114235336700_ref105","doi-asserted-by":"crossref","first-page":"199","DOI":"10.2307\/1970311","article-title":"On gradient dynamical systems","volume":"74","author":"Smale","year":"1961","journal-title":"Annals of Mathematics"},{"key":"2026033114235336700_ref106","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511530043","volume-title":"The Theory of the Chemostat: Dynamics of Microbial Competition","author":"Smith","year":"1995"},{"issue":"2","key":"2026033114235336700_ref107","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01362149","article-title":"A Nullstellensatz and a positivstellensatz in semialgebraic geometry","volume":"207","author":"Stengle","year":"1974","journal-title":"Mathematische Annalen"},{"issue":"11","key":"2026033114235336700_ref108","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0895-7177(96)00064-7","article-title":"A logical DES approach to the design of hybrid control systems","volume":"23","author":"Stiver","year":"1996","journal-title":"Mathematical and Computer Modelling"},{"key":"2026033114235336700_ref109","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","article-title":"Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones","volume":"11","author":"Sturm","year":"1999","journal-title":"Optimization Method & Software"},{"issue":"1","key":"2026033114235336700_ref110","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.tree.2003.10.005","article-title":"\u2018Alternative states and positive feedbacks in restoration ecology","volume":"19","author":"Suding","year":"2004","journal-title":"Trends in Ecology & Evolution"},{"issue":"5","key":"2026033114235336700_ref111","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.tree.2008.11.012","article-title":"Threshold models in restoration and conservation: A developing framework","volume":"24","author":"Suding","year":"2009","journal-title":"Trends in Ecology & Evolution"},{"key":"2026033114235336700_ref112","author":"Tamba","year":"2015"},{"key":"2026033114235336700_ref113","doi-asserted-by":"crossref","first-page":"2697","DOI":"10.1109\/CDC.2013.6760290","article-title":"Using first passage times to manage eco-system regime shifts","author":"Tamba","year":"2013","journal-title":"IEEE Conference on Decision and Control"},{"key":"2026033114235336700_ref114","article-title":"The distance-to-bifurcation problem in non-negative dynamical systems with kinetic realizations","author":"Tamba","year":"2014","journal-title":"IEEE International Conference on Control and Automation (ICCA)"},{"key":"2026033114235336700_ref115","volume-title":"American Control Conference","author":"Tan","year":"2006"},{"issue":"19","key":"2026033114235336700_ref116","doi-asserted-by":"crossref","first-page":"2229","DOI":"10.1093\/bioinformatics\/btn401","article-title":"Large-scale computation of elementary flux modes with bit pattern trees","volume":"24","author":"Terzer","year":"2008","journal-title":"Bioinformatics"},{"issue":"1\u20134","key":"2026033114235336700_ref117","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1080\/10556789908805762","article-title":"SDPT3\u2014A MAT-LAB software package for semidefinite programming, version 1.3","volume":"11","author":"Toh","year":"1999","journal-title":"Optimization Methods and Software"},{"issue":"2","key":"2026033114235336700_ref118","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.mbs.2007.02.006","article-title":"Heteroclinic orbits indicate overexploitation in predator\u2013prey systems with a strong allee effect","volume":"209","author":"Van Voorn","year":"2007","journal-title":"Mathematical Biosciences"},{"issue":"1","key":"2026033114235336700_ref119","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","article-title":"Semidefinite programming","volume":"38","author":"Vandenberghe","year":"1996","journal-title":"SIAM Review"},{"issue":"4","key":"2026033114235336700_ref120","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","article-title":"A tutorial on spectral clustering","volume":"17","author":"Von Luxburg","year":"2007","journal-title":"Statistics and Computing"},{"key":"2026033114235336700_ref121","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139856065","volume-title":"Modern Computer Algebra","author":"Von Zur Gathen","year":"2013"},{"key":"2026033114235336700_ref122","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1080\/00207720902957269","article-title":"Searching bifurcations in highdimensional parameter space via a feedback loop breaking approach","volume":"40","author":"Waldherr","year":"2009","journal-title":"International Journal of System Science"},{"key":"2026033114235336700_ref123","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","author":"Wiggins","year":"2003"},{"issue":"6774","key":"2026033114235336700_ref124","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1038\/35004572","article-title":"Simple rules yield complex food webs","volume":"404","author":"Williams","year":"2000","journal-title":"Nature"},{"key":"2026033114235336700_ref125","first-page":"461","volume-title":"IEEE Conference on Decision and Control","author":"Yazarel","year":"2004"},{"issue":"6","key":"2026033114235336700_ref126","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1086\/285380","article-title":"Body size and consumer-resource dynamics","volume":"139","author":"Yodzis","year":"1992","journal-title":"American Naturalist"}],"container-title":["Foundations and Trends\u00ae in Systems and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftsys\/article-pdf\/7\/4\/384\/11149251\/2600000021en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftsys\/article-pdf\/7\/4\/384\/11149251\/2600000021en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:00:45Z","timestamp":1777489245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftsys\/article\/7\/4\/384\/1332193\/Achieving-Ecological-Resilience-Through-Regime"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,19]]},"references-count":126,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,8,19]]}},"URL":"https:\/\/doi.org\/10.1561\/2600000021","relation":{},"ISSN":["2325-6818","2325-6826"],"issn-type":[{"value":"2325-6818","type":"print"},{"value":"2325-6826","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,19]]}}}