期刊
出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-030-34724-6_31
关键词
Fractional-order difference equation; Caputo fractional difference; Fractional-order Rulkov model; Neuronal model; Incommensurate fractional-order system
资金
- COST (European Cooperation in Science and Technology) [CA15225]
- Polish funds of National Science Center [DEC2016/23/B/ST7/03686]
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.
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