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Title: Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems
Authors: Datsko, Bohdan
Luchko, Yuri
Keywords: fractional dynamical system
linear stability analysis
limit cycles
fractional FitzHugh-Nagumo model
Issue Date: 2012
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 65p-78p
Abstract: In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to ones in the systems with integer order derivatives. As an example, the incommensurate fractional FitzHugh-Nagumo model is considered. For this model, different kinds of limit cycles are obtained by the method of computer simulation. A common picture of non-linear dynamics in fractional dynamical systems with positive and negative feedbacks is presented.
Description: MSC 2010: 26A33, 34D05, 37C25
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 26, 2012, Fasc. 1-2

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