Multistability in nonlinearly coupled ring of Duffing systems

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.