Volume 134, Number 3, May 2021
|Number of page(s)||7|
|Published online||15 July 2021|
Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping
1 Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara Enrique Díaz de León 1144, Colonia Paseos de la Montaña, Lagos de Moreno, Jalisco, Mexico
2 Lobachevsky State University of Nizhny Novgorod - Nizhny Novgorod, Russia
3 Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, Campus de Montegancedo - Pozuelo de Alarcón, 28223 Madrid, Spain
4 Innopolis University - Universitetskaya Str. 1, 420500 Innopolis, Republic of Tatarstan, Russia
(a) firstname.lastname@example.org (corresponding author)
Received: 1 March 2021
Accepted: 14 April 2021
We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed, proportional to time, and inversely proportional to time. The system dynamics in all cases are analyzed using time series, Fourier and Hilbert transforms, Poincaré sections, bifurcation diagrams, and Lyapunov exponents for various coupling strengths and damping coefficients. In the first case, we observe a well-known route from a stable steady state to hyperchaos through Hopf bifurcation and a series of torus bifurcations, as the coupling strength is increased. In the second case, the system is highly dissipative and converges into one of the stable equilibria. Finally, in the third case, transient toroidal hyperchaos takes place.
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