# Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

Mathematica Balkanica New Series (2012)

- Volume: 26, Issue: 1-2, page 65-78
- ISSN: 0205-3217

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topDatsko, Bohdan, and Luchko, Yuri. "Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems." Mathematica Balkanica New Series 26.1-2 (2012): 65-78. <http://eudml.org/doc/281372>.

@article{Datsko2012,

abstract = {MSC 2010: 26A33, 34D05, 37C25In 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.},

author = {Datsko, Bohdan, Luchko, Yuri},

journal = {Mathematica Balkanica New Series},

keywords = {fractional dynamical system; linear stability analysis; limit cycles; fractional FitzHugh-Nagumo model},

language = {eng},

number = {1-2},

pages = {65-78},

publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},

title = {Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems},

url = {http://eudml.org/doc/281372},

volume = {26},

year = {2012},

}

TY - JOUR

AU - Datsko, Bohdan

AU - Luchko, Yuri

TI - Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

JO - Mathematica Balkanica New Series

PY - 2012

PB - Bulgarian Academy of Sciences - National Committee for Mathematics

VL - 26

IS - 1-2

SP - 65

EP - 78

AB - MSC 2010: 26A33, 34D05, 37C25In 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.

LA - eng

KW - fractional dynamical system; linear stability analysis; limit cycles; fractional FitzHugh-Nagumo model

UR - http://eudml.org/doc/281372

ER -

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