Repertoire of dynamical states in dissimilarly coupled Van der Pol oscillators

• Published in: Chaos, solitons and fractals solitons and fractals, 2024-02, Vol.179, p.114421, Article 114421
• Main Authors: Manoranjani, M., Subashree, B., Senthilkumar, D.V., Chandrasekar, V.K.
• Format: Article
• Language: English
• Subjects: Dissimilar coupling; Intermittency route to chaos; Symmetry breaking states; Van der Pol oscillators
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2023.114421

We have considered dissimilarly coupled Van der Pol oscillators with an offset parameter which determines the degree of heterogeneity of the dissimilar coupling strength. Increasing degree of heterogeneity for decreasing values of the offset parameter results in a rich repertoire of bifurcation transitions and dynamical states including epochs of period doubling bifurcation. Two distinct multi-stable states are also observed along with several symmetry breaking dynamical states. We have deduced analytical stability conditions for Hopf and pitch-fork bifurcations through a linear stability analysis of symmetry preserving states, namely, trivial steady state and oscillation death state. The analytical conditions are found to match exactly with the simulation results in the two-parameter phase diagram. In addition to torus bifurcation, crisis and crisis induced intermittency routes to chaos are also observed for an appropriate heterogeneity of the dissimilar coupling strength. The period doubling bifurcation is characterized using the largest Lyapunov exponents of the dissimilarly coupled Van der Pol oscillators. •Increasing the degree of heterogeneity yields a diverse range of bifurcation transitions and dynamic states, including periods of doubling bifurcations.•In-phase oscillatory states coexist with both symmetry-breaking and out-phase oscillatory states.•The period-doubling bifurcation is characterized using the largest Lyapunov exponents.•Appropriate heterogeneity levels in coupling lead to chaotic behaviors via crises and intermittency bifurcation.•Deduced stability conditions for Hopf and pitch-fork bifurcations through linear stability analysis.