Stability of Systems of Fractional-Order Difference Equations and Applications to a Rulkov-Type Neuronal Model

被引：5

作者：

Brandibur, Oana ^{[1
]}

Kaslik, Eva ^{[1
]}

Mozyrska, Dorota ^{[2
]}

Wyrwas, Malgorzata ^{[2
]}

机构：

[1] West Univ Timisoara, Dept Math & Comp Sci, Timisoara, Romania

[2] Bialystok Tech Univ, Fac Comp Sci, Bialystok, Poland

来源：

NEW TRENDS IN NONLINEAR DYNAMICS, VOL III: PROCEEDINGS OF THE FIRST INTERNATIONAL NONLINEAR DYNAMICS CONFERENCE (NODYCON 2019) | 2020年

关键词：

Fractional-order difference equation; Caputo fractional difference; Fractional-order Rulkov model; Neuronal model; Incommensurate fractional-order system;

D O I：

10.1007/978-3-030-34724-6_31

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Necessary and sufficient conditions for the asymptotic stability and instability of two-dimensional linear autonomous incommensurate systems of fractional-order Caputo difference equations are presented. Moreover, the occurrence of discrete Flip and Hopf bifurcations is also discussed, choosing the fractional orders as bifurcation parameters. The theoretical results are then applied to the investigation of the stability and instability properties of a fractional-order version of the Rulkov neuronal model. Numerical simulations are further presented to illustrate the theoretical findings, revealing complex bursting behavior in the fractional-order Rulkov model.

引用

页码：305 / 314

页数：10

共 10 条

[1] THE FRACTIONAL-ORDER DYNAMICS OF BRAIN-STEM VESTIBULOOCULOMOTOR NEURONS [J].