{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T14:45:51Z","timestamp":1773326751004,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,10,12]],"date-time":"2014-10-12T00:00:00Z","timestamp":1413072000000},"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":["Dyn Games Appl"],"published-print":{"date-parts":[[2015,9]]},"DOI":"10.1007\/s13235-014-0124-0","type":"journal-article","created":{"date-parts":[[2014,10,13]],"date-time":"2014-10-13T05:30:00Z","timestamp":1413178200000},"page":"318-333","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex"],"prefix":"10.1007","volume":"5","author":[{"given":"Marc","family":"Harper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dashiell","family":"Fryer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,10,12]]},"reference":[{"issue":"1","key":"124_CR1","first-page":"183","volume":"58","author":"S Amari","year":"2010","unstructured":"Amari S, Cichocki A (2010) Information geometry of divergence functions. Bull Pol Acad Sci 58(1):183\u2013195","journal-title":"Bull Pol Acad Sci"},{"key":"124_CR2","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/191","volume-title":"Methods of information geometry","author":"S Amari","year":"2007","unstructured":"Amari S, Nagaoka H (2007) Methods of information geometry, vol 191. American Mathematical Society, Providence"},{"issue":"03","key":"124_CR3","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/10236190902932734","volume":"17","author":"Z Bartosiewicz","year":"2011","unstructured":"Bartosiewicz Z, Piotrowska E (2011) Lyapunov functions in stability of nonlinear systems on time scales. J Differ Equ Appl 17(03):309\u2013325","journal-title":"J Differ Equ Appl"},{"key":"124_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0201-1","volume-title":"Dynamic equations on time scales","author":"M Bohner","year":"2001","unstructured":"Bohner M, Peterson A (2001) Dynamic equations on time scales, vol 160. Springer, Boston"},{"key":"124_CR5","volume-title":"Advances in dynamic equations on time scales","author":"M Bohner","year":"2002","unstructured":"Bohner M, Peterson A (2002) Advances in dynamic equations on time scales. Springer, Boston"},{"issue":"1","key":"124_CR6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF00168008","volume":"30","author":"I Bomze","year":"1991","unstructured":"Bomze I (1991) Cross entropy minimization in uninvadable states of complex populations. J Math Biol 30(1):73\u201387","journal-title":"J Math Biol"},{"issue":"1","key":"124_CR7","first-page":"374","volume":"13","author":"G Brown","year":"1951","unstructured":"Brown G (1951) Iterative solution of games by fictitious play. Act Anal Prod Alloc 13(1):374\u2013376","journal-title":"Act Anal Prod Alloc"},{"issue":"1","key":"124_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0165-4896(97)00009-7","volume":"34","author":"R Cressman","year":"1997","unstructured":"Cressman R (1997) Local stability of smooth selection dynamics for normal form games. Math Soc Sci 34(1):1\u201319","journal-title":"Math Soc Sci"},{"key":"124_CR9","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2884.001.0001","volume-title":"Evolutionary dynamics and extensive form games","author":"R Cressman","year":"2003","unstructured":"Cressman R (2003) Evolutionary dynamics and extensive form games, vol 5. MIT Press, Cambridge"},{"issue":"2","key":"124_CR10","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.cam.2004.07.026","volume":"176","author":"J DaCunha","year":"2005","unstructured":"DaCunha J (2005) Stability for time varying linear dynamic systems on time scales. J Comput Appl Math 176(2):381\u2013410","journal-title":"J Comput Appl Math"},{"key":"124_CR11","doi-asserted-by":"crossref","unstructured":"Davis J, Gravagne I, Marks R, Ramos A (2010) Algebraic and dynamic lyapunov equations on time scales. In: 42nd Southeastern Symposium on System Theory (SSST), pp 329\u2013334. IEEE","DOI":"10.1109\/SSST.2010.5442815"},{"key":"124_CR12","unstructured":"Fryer D (2012) The Kullback-Leibler divergence as a Lyapunov function for incentive based game dynamics. arXiv preprint arXiv:1207.0036"},{"key":"124_CR13","unstructured":"Fryer D (2012) On the existence of general equilibrium in finite games and general game dynamics. arXiv preprint arXiv:1201.2384"},{"key":"124_CR14","volume-title":"The theory of learning in games","author":"D Fudenberg","year":"1998","unstructured":"Fudenberg D (1998) The theory of learning in games, vol 2. MIT press, Cambridge"},{"issue":"18","key":"124_CR15","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1016\/j.physd.2011.04.008","volume":"240","author":"M Harper","year":"2011","unstructured":"Harper M (2011) Escort evolutionary game theory. Physica D 240(18):1411\u20131415","journal-title":"Physica D"},{"issue":"78","key":"124_CR16","doi-asserted-by":"crossref","first-page":"20120758","DOI":"10.1098\/rsif.2012.0758","volume":"10","author":"A Hernando","year":"2013","unstructured":"Hernando A, Hernando R, Plastino A, Plastino AR (2013) The workings of the maximum entropy principle in collective human behaviour. J R Soc Interface 10(78):20120758","journal-title":"J R Soc Interface"},{"key":"124_CR17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/psapm\/069\/2882634","volume-title":"Deterministic evolutionary game dynamics","author":"J Hofbauer","year":"2011","unstructured":"Hofbauer J (2011) Deterministic evolutionary game dynamics, vol 69. American Mathematical Society, New Orleans, pp 61\u201369"},{"issue":"4","key":"124_CR18","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0893-9659(90)90051-C","volume":"3","author":"J Hofbauer","year":"1990","unstructured":"Hofbauer J, Sigmund K (1990) Adaptive dynamics and evolutionary stability. Appl Math Lett 3(4):75\u201379","journal-title":"Appl Math Lett"},{"key":"124_CR19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary games and population dynamics","author":"J Hofbauer","year":"1998","unstructured":"Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge"},{"issue":"4","key":"124_CR20","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1090\/S0273-0979-03-00988-1","volume":"40","author":"J Hofbauer","year":"2003","unstructured":"Hofbauer J, Sigmund K (2003) Evolutionary game dynamics. Bull Am Math Soc 40(4):479\u2013519","journal-title":"Bull Am Math Soc"},{"key":"124_CR21","first-page":"8","volume-title":"Game theory and applications","author":"R Joosten","year":"2013","unstructured":"Joosten R (2013) Paul samuelson\u2019s critique and equilibrium concepts in evolutionary game theory. In: Petrosjan L, Mazalov V (eds) Game theory and applications, vol 16. NOVA Publishers, New York, p 8"},{"key":"124_CR22","unstructured":"Joosten R, Roorda B (2008) Generalized projection dynamics in evolutionary game theory. Technical report, Papers on economics and evolution"},{"issue":"2","key":"124_CR23","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s00186-010-0342-1","volume":"74","author":"R Joosten","year":"2011","unstructured":"Joosten R, Roorda B (2011) On evolutionary ray-projection dynamics. Math Methods Oper Res 74(2):147\u2013161","journal-title":"Math Methods Oper Res"},{"issue":"2","key":"124_CR24","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.geb.2008.02.002","volume":"64","author":"R Lahkar","year":"2008","unstructured":"Lahkar R, Sandholm W (2008) The projection dynamic and the geometry of population games. Games Econ Behav 64(2):565\u2013590","journal-title":"Games Econ Behav"},{"issue":"2","key":"124_CR25","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0022-0531(92)90040-O","volume":"57","author":"A Matsui","year":"1992","unstructured":"Matsui A (1992) Best response dynamics and socially stable strategies. J Ecoomic Theory 57(2):343\u2013362","journal-title":"J Ecoomic Theory"},{"key":"124_CR26","volume-title":"Projected dynamical systems and variational inequalities with applications","author":"A Nagurney","year":"1995","unstructured":"Nagurney A, Zhang D (1995) Projected dynamical systems and variational inequalities with applications, vol 2. Springer, Berlin"},{"issue":"2","key":"124_CR27","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1287\/trsc.31.2.147","volume":"31","author":"A Nagurney","year":"1997","unstructured":"Nagurney A, Zhang D (1997) Projected dynamical systems in the formulation, stability analysis, and computation of fixed-demand traffic network equilibria. Transport Sci 31(2):147\u2013158","journal-title":"Transport Sci"},{"issue":"4","key":"124_CR28","first-page":"102","volume":"5","author":"J Naudts","year":"2004","unstructured":"Naudts J (2004) Estimators, escort probabilities, and phi-exponential families in statistical physics. J Ineq Pure Appl Math 5(4):102","journal-title":"J Ineq Pure Appl Math"},{"key":"124_CR29","volume-title":"Population games and evolutionary dynamics","author":"W Sandholm","year":"2011","unstructured":"Sandholm W (2011) Population games and evolutionary dynamics. MIT press, Cambridge"},{"issue":"2","key":"124_CR30","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1016\/j.geb.2008.02.003","volume":"64","author":"W Sandholm","year":"2008","unstructured":"Sandholm W, Dokumac\u0131 E, Lahkar R (2008) The projection dynamic and the replicator dynamic. Games Econ Behav 64(2):666\u2013683","journal-title":"Games Econ Behav"},{"key":"124_CR31","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1090\/psapm\/069\/2882635","volume":"69","author":"S Sorin","year":"2012","unstructured":"Sorin S (2012) On some global and unilateral adaptive dynamics. AMS Short Course Evol Game Dyn 69:81\u2013110","journal-title":"AMS Short Course Evol Game Dyn"},{"issue":"1","key":"124_CR32","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0025-5564(78)90077-9","volume":"40","author":"P Taylor","year":"1978","unstructured":"Taylor P, Jonker L (1978) Evolutionary stable strategies and game dynamics. Math Biosci 40(1):145\u2013156","journal-title":"Math Biosci"},{"issue":"1","key":"124_CR33","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","volume":"52","author":"C Tsallis","year":"1988","unstructured":"Tsallis C (1988) Possible generalization of boltzmann-gibbs statistics. J Stat Phys 52(1):479\u2013487","journal-title":"J Stat Phys"},{"key":"124_CR34","volume-title":"Evolutionary game theory","author":"J Weibull","year":"1997","unstructured":"Weibull J (1997) Evolutionary game theory. MIT press, Cambridge"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-014-0124-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13235-014-0124-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-014-0124-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T03:54:47Z","timestamp":1565927687000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13235-014-0124-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,12]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["124"],"URL":"https:\/\/doi.org\/10.1007\/s13235-014-0124-0","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"value":"2153-0785","type":"print"},{"value":"2153-0793","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,12]]}}}