The transition from bursting to continuous spiking in excitable membrane models

Autor:	D. Terman
Rok vydání:	1992
Předmět:	Discrete mathematics Fibonacci number Mathematical model Applied Mathematics General Engineering Theta model Bursting Modeling and Simulation Hindmarsh–Rose model Statistical physics Invariant (mathematics) Topological conjugacy Bifurcation Mathematics
Zdroj:	Journal of Nonlinear Science. 2:135-182
ISSN:	1432-1467 0938-8974
DOI:	10.1007/bf02429854
Popis:	Mathematical models for excitable membranes may exhibit bursting solutions, and, for different values of the parameters, the bursting solutions give way to continuous spiking. Numerical results have demonstrated that during the transition from bursting to continuous spiking, the system of equations may give rise to very complicated dynamics. The mathematical mechanism responsible for this dynamics is described. We prove that during the transition from bursting to continuous spiking the system must undergo a large number of bifurcations. After each bifurcation the system is increasingly chaotic in the sense that the maximal invariant set of a certain two-dimensional map is topologically equivalent to the shift on a larger set of symbols. The number of symbols is related to the Fibonacci numbers.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c90222fa05bcc6a2e13770378a26d58b https://doi.org/10.1007/bf02429854 Zobrazit plný text záznamu Full text from SpringerLink