https://doi.org/10.1140/epjst/e2016-60015-7
Regular Article
Multistability in nonlinearly coupled ring of Duffing systems
Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
a e-mail: przemyslaw.perlikowski@p.lodz.pl
Received: 30 January 2016
Revised: 7 June 2016
Published online: 22 November 2016
In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation's scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters’ bifurcation diagrams with marked areas where one can observe the coexistence of solutions.
© The Author(s) 2016
Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
