{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T17:24:48Z","timestamp":1648661088059},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,5,10]],"date-time":"2014-05-10T00:00:00Z","timestamp":1399680000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biol Cybern"],"published-print":{"date-parts":[[2014,6]]},"DOI":"10.1007\/s00422-014-0605-7","type":"journal-article","created":{"date-parts":[[2014,5,9]],"date-time":"2014-05-09T04:06:10Z","timestamp":1399608370000},"page":"365-380","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fixed-point bifurcation analysis in biological models using interval polynomials theory"],"prefix":"10.1007","volume":"108","author":[{"given":"Gerasimos G.","family":"Rigatos","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,5,10]]},"reference":[{"key":"605_CR1","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1016\/j.cnsns.2011.09.028","volume":"17","author":"M Aqil","year":"2012","unstructured":"Aqil M, Hong KS, Jeong MY (2012) Synchronization of coupled chaotic FitzHugh\u2013Nagumo systems. Commun Nonlinear Sci Numer Simul 17:1615\u20131627","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"605_CR2","volume-title":"Mathematical foundations of neuroscience","author":"G Baird Emertrout","year":"2009","unstructured":"Baird Emertrout G, Terman DH (2009) Series in interdisciplinary applied Mathematics. Mathematical foundations of neuroscience. Springer, Berlin"},{"issue":"3","key":"605_CR3","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1142\/S0218127400000360","volume":"10","author":"G Chen","year":"2000","unstructured":"Chen G, Moiola JL, Wang HO (2000) Bifurcation control: theories methods and applications. Int J Bifurc Chaos 10(3):511\u2013548","journal-title":"Int J Bifurc Chaos"},{"key":"605_CR4","doi-asserted-by":"crossref","unstructured":"Clairambault J (2006) Physiologically based modelling of circadian control on cell proliferation. In: 28th IEEE EMBS annual international conference, New York, USA, Sep 2006","DOI":"10.1109\/IEMBS.2006.260855"},{"issue":"1","key":"605_CR5","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MEMB.2007.907363","volume":"27","author":"J Clairambault","year":"2008","unstructured":"Clairambault J (2008) A step toward optimization of cancer therapeutics: physiologically based modeling of circadian control on cell proliferation. IEEE Eng Med Biol Mag 27(1):20\u201324","journal-title":"IEEE Eng Med Biol Mag"},{"key":"605_CR6","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.chaos.2013.04.003","volume":"52","author":"RO Dorak","year":"2013","unstructured":"Dorak RO (2013) Control of repetitive firing in Hodgkin\u2013Huxley nerve fibers using electric fields. Chaos, Solitons and Fractals 52:66\u201372","journal-title":"Chaos, Solitons and Fractals"},{"key":"605_CR7","doi-asserted-by":"crossref","first-page":"600","DOI":"10.4028\/www.scientific.net\/AMR.485.600","volume":"485","author":"H Duan","year":"2012","unstructured":"Duan H, Cai C, Han C, Che Y (2012) Bifurcation control in Morris\u2013Lecar neuron model via washout filter with a linear term based on filter-aided dynamic feedback. Adv Mater Res 485:600\u2013603","journal-title":"Adv Mater Res"},{"key":"605_CR8","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.automatica.2005.09.018","volume":"42","author":"DV Efimov","year":"2006","unstructured":"Efimov DV, Fradkov AL (2006) Adaptive tuning to bifurcation for time-varying nonlinear systems. Automatica 42:417\u2013425","journal-title":"Automatica"},{"key":"605_CR9","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1529\/biophysj.104.053975","volume":"88","author":"P Francois","year":"2005","unstructured":"Francois P (2005) A model for the Neurospora circadian clock. Biophys J 88:2369\u20132383","journal-title":"Biophys J"},{"key":"605_CR10","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511815706","volume-title":"Spiking neuron models: single neurons, populations, plasticity","author":"W Gerstner","year":"2002","unstructured":"Gerstner W, Kistler W (2002) Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, Cambridge"},{"key":"605_CR11","first-page":"57","volume":"323","author":"D Gonze","year":"2000","unstructured":"Gonze D, Leloup JC, Goldbeter A (2000) Theoretical models for circadian rhythms in Neurospora and Drosophila. C R Acad Sci Paris, Sciences de la Vie \/ Life Sciences 323:57\u201367","journal-title":"C R Acad Sci Paris, Sciences de la Vie \/ Life Sciences"},{"issue":"2","key":"605_CR12","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1073\/pnas.022628299","volume":"99","author":"D Gonze","year":"2002","unstructured":"Gonze D, Halloy Jos\u00e9 (2002) Robustness of circadian rhythms with respect to molecular noise. Proc Natl Acad Sci 99(2):673\u2013678","journal-title":"Proc Natl Acad Sci"},{"key":"605_CR13","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S1631-0691(03)00016-7","volume":"326","author":"D Gonze","year":"2003","unstructured":"Gonze D, Halloy J, Leloup JC, Goldbeter A (2003) Stochastic models for circadian rhythmes: effect of molecular noise on periodic and chaotic behaviour. C R Biol 326:189\u2013203","journal-title":"C R Biol"},{"key":"605_CR14","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.neucom.2004.11.030","volume":"64","author":"R Haschke","year":"2005","unstructured":"Haschke R, Steil JJ (2005) Input-space bifurcation manifolds of recurrent neural networks. Neurocomputing 64:25\u201338","journal-title":"Neurocomputing"},{"key":"605_CR15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.neunet.2003.09.003","volume":"17","author":"M Lysetskiy","year":"2004","unstructured":"Lysetskiy M, Zurada JM (2004) Bifurcating neuron: computation and learning. Neural Netw 17:225\u2013232","journal-title":"Neural Netw"},{"key":"605_CR16","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1016\/j.apm.2007.03.013","volume":"38","author":"B Nagy","year":"2008","unstructured":"Nagy B (2008) Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model. Appl Math Model 38:1587\u20131598","journal-title":"Appl Math Model"},{"issue":"2","key":"605_CR17","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1109\/TAC.2003.822859","volume":"49","author":"B Laroche","year":"2004","unstructured":"Laroche B, Claude D (2004) Flatness-based control of PER protein oscillations in a Drosophila model. IEEE Trans Autom Control 49(2):175\u2013183","journal-title":"IEEE Trans Autom Control"},{"issue":"6","key":"605_CR18","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1177\/074873099129000948","volume":"14","author":"JC Leloup","year":"1999","unstructured":"Leloup JC, Gonze D, Goldbeter A (1999) Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J Biol Rhythms 14(6):433\u2013448","journal-title":"J Biol Rhythms"},{"key":"605_CR19","volume-title":"Computational Systems Biology","author":"JC Leloup","year":"2006","unstructured":"Leloup JC, Gonze D, Goldbeter A (2006) Computational models for circadian rythms: deterministic versus stochastic approaches. Computational Systems Biology. Elsevier, Amsterdam"},{"key":"605_CR20","doi-asserted-by":"crossref","unstructured":"Lee JH, Sancar A (2011) Circadian clock disruption improves the efficacy of chemotherapy through p73-mediated apoptosis. In: Proceedings of the National Academy of Sciences","DOI":"10.1073\/pnas.1106284108"},{"issue":"1","key":"605_CR21","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/MEMB.2007.907361","volume":"27","author":"FA L\u00e9vi","year":"2008","unstructured":"L\u00e9vi FA (2008) The circadian timing system: a coordinator of life processes. IEEE Eng Med Biol Mag 27(1):17\u201319","journal-title":"IEEE Eng Med Biol Mag"},{"key":"605_CR22","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0167-2789(00)00197-4","volume":"149","author":"X Liao","year":"2001","unstructured":"Liao X, Wong KW, Wu Z (2001) Bifurcation analysis of a two-neuron system with distributed delays. Phys D 149:123\u2013141","journal-title":"Phys D"},{"key":"605_CR23","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.cam.2008.08.006","volume":"226","author":"B Nagy","year":"2009","unstructured":"Nagy B (2009) Analysis of the biological clock of Neurospora. J Comput Appl Math 226:298\u2013305","journal-title":"J Comput Appl Math"},{"key":"605_CR24","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.physleta.2011.11.057","volume":"376","author":"LH Nguyen","year":"2012","unstructured":"Nguyen LH, Hong KS (2012) Hopf bifurcation control via a dynamic state-feedback control. Phys Lett A 376:442\u2013446","journal-title":"Phys Lett A"},{"key":"605_CR25","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s00422-012-0508-4","volume":"106","author":"LH Nguyen","year":"2012","unstructured":"Nguyen LH, Hong KS, Park S (2012) Bifurcation control of the Morris\u2013Lecar neuron model via a dynamic state feedback ontrol. Biol Cybern 106:587\u2013594","journal-title":"Biol Cybern"},{"issue":"1","key":"605_CR26","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.matcom.2010.07.008","volume":"82","author":"GG Rigatos","year":"2011","unstructured":"Rigatos GG, Siano P (2011) Design of robust electric power system stabilizers using Kharitonov\u2019s theorem. Math Comput Simul 82(1):181\u2013191","journal-title":"Math Comput Simul"},{"key":"605_CR27","doi-asserted-by":"crossref","unstructured":"Rigatos G, Rigatou E (2013) A Kalman Filtering approach to robust synchronization of coupled neural oscillators. In: ICNAAM 2013, 11th international conference on numerical analysis and applied mathematics, Rhodes, Greece, Sep. 2013","DOI":"10.1063\/1.4826063"},{"key":"605_CR28","volume-title":"Advanced models of neural networks: nonlinear dynamics and stochasticity in biological neurons","author":"GG Rigatos","year":"2013","unstructured":"Rigatos GG (2013) Advanced models of neural networks: nonlinear dynamics and stochasticity in biological neurons. Springer, Berlin"},{"key":"605_CR29","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.physd.2004.10.010","volume":"200","author":"Y Song","year":"2005","unstructured":"Song Y, Han M, Wei J (2005) Stability and Hopf bifurcation analysis on a simplified BAM network with delays. Phys D 200:185\u2013204","journal-title":"Phys D"},{"issue":"4","key":"605_CR30","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1177\/0142331212453597","volume":"35","author":"LT That","year":"2012","unstructured":"That LT, Ding Z (2012) Reduced-order observer design of multi-output nonlinear systems with application to a circadian model. Trans Inst Meas Control 35(4):417\u2013425","journal-title":"Trans Inst Meas Control"},{"key":"605_CR31","first-page":"20232028","volume":"180","author":"R Toscano","year":"2010","unstructured":"Toscano R, Lyonnet P (2010) Robust static output feedback controller synthesis using Kharitonov\u2019s theorem and evolutionary algorithms. Inf Sci 180:20232028","journal-title":"Inf Sci"},{"key":"605_CR32","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.jtbi.2005.07.017","volume":"239","author":"K Tsumoto","year":"2006","unstructured":"Tsumoto K, Yoshinaga T, Iida H, Kawakami H, Ashara K (2006) Bifurcations in a mathematical model for circadian oscillations of clock genes. J Theor Biol 239:101\u2013122","journal-title":"J Theor Biol"},{"issue":"7","key":"605_CR33","doi-asserted-by":"crossref","first-page":"e39001","DOI":"10.1371\/journal.pone.0039001","volume":"7","author":"A Vidal","year":"2012","unstructured":"Vidal A, Zhang Q, M\u00e9digue C, Fabre S, Cl\u00e9ment F (2012) DynPeak: An Algorithm for Pulse Detection and Frequency Analysis in Hormonal Time Series. PLoS One 7(7):e39001","journal-title":"PLoS One"},{"key":"605_CR34","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.chaos.2006.01.035","volume":"33","author":"J Wang","year":"2004","unstructured":"Wang J, Chen L, Fei X (2004) Bifurcation control of the Hodgkin-Huxley equations. Chaos, Solitons and Fractals 33:217\u2013224","journal-title":"Chaos, Solitons and Fractals"},{"key":"605_CR35","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.cnsns.2012.06.022","volume":"18","author":"H Wang","year":"2013","unstructured":"Wang H, Yu Y, Zhu R, Wang S (2013) Two-parameter bifurcation in a two-dimensional simplified Hodgkin\u2013Huxley model. Commun Nonlinear Sci Numer Simul 18:184\u2013193","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"605_CR36","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.physleta.2006.01.034","volume":"354","author":"X Xu","year":"2006","unstructured":"Xu X, Hu HY, Wang HL (2006) Stability switches, Hopf bifurcations and chaos of a neuron model with delay dependent parameters. Phys Lett A 354:126\u2013136","journal-title":"Phys Lett A"},{"key":"605_CR37","doi-asserted-by":"crossref","unstructured":"Zhang J, Bierman A, Wen JT, Julius A, Figueiro M (2010) Circadian system modeling and phase control. In: 49th IEEE conference on decision and control, Dec. 2010","DOI":"10.1109\/CDC.2010.5718105"},{"issue":"1","key":"605_CR38","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.chaos.2006.01.037","volume":"33","author":"T Zhang","year":"2007","unstructured":"Zhang T, Wang J, Fei X, Deng B (2007) Synchronization of coupled FitzHugh\u2013Nagumo systems via MIMO feedback linearization control. Chaos Solitons and Fractals 33(1):194\u2013202","journal-title":"Chaos Solitons and Fractals"}],"container-title":["Biological Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-014-0605-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00422-014-0605-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-014-0605-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T05:31:23Z","timestamp":1565415083000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00422-014-0605-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,10]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["605"],"URL":"https:\/\/doi.org\/10.1007\/s00422-014-0605-7","relation":{},"ISSN":["0340-1200","1432-0770"],"issn-type":[{"value":"0340-1200","type":"print"},{"value":"1432-0770","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,10]]}}}