Dynamics of a ring of three fractional-order Duffing oscillators

被引：17

作者：

Barba-Franco, J. J. ^{[1
]}

Gallegos, A. ^{[1
]}

Jaimes-Reategui, R. ^{[1
]}

Pisarchik, A. N. ^{[2
,3
]}

机构：

[1] Univ Guadalajara, Ctr Univ Lagos, Dept Ciencias Exactas & Tecnol, Enr Diaz de Leon 1144, Lagos De Moreno, Jalisco, Mexico

[2] Univ Politecn Madrid, Ctr Tecnol Biomed, Campus Montegancedo, Madrid 28223, Spain

[3] Innopolis Univ, Univ Skaya Str 1, Innopolis 420500, Republic Of Tat, Russia

来源：

CHAOS SOLITONS & FRACTALS | 2022年 / 155卷

关键词：

Duffing oscillator; Unidirectional coupling; Fractional-order differential equations; Multistability; Grundwall-Letnikov derivative; ROTATING WAVES; SYNCHRONIZATION; RESONANCE; CHAOS; MODEL;

D O I：

10.1016/j.chaos.2021.111747

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the dynamics of three ring-coupled double-well Duffing oscillators modelled by fractional-order differential equations. The analysis of time series, Fourier spectra, phase portraits, Poincare sec-tions, and Lyapunov exponents using the fractional order and the coupling strength as control parameters, shows that the dynamics of such system is much richer than that of the system with integer order. We demonstrate the appearance of multistability and a rotating wave when either the fractional derivative index or the coupling strength is increased, on the route from a stable steady-state regime to hyperchaos through a Hopf bifurcation and a cascade of torus bifurcations.(c) 2021 Elsevier Ltd. All rights reserved.

引用

页数：7

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