Multistable dynamics and chaos in a system consisting of an inertial neuron coupled to a van der Pol oscillator

Abstract

Abstract We consider a dynamical system consisting of a van der Pol oscillator linearly coupled to an inertial neuron with two wells potential. Analytical studies are conducted focusing on the energy computation, the dissipation and symmetry, as well as the determination and characterization of the equilibrium points. We define the parameter ranges related to different types of oscillations in the coupled system in order to have an overall idea of the nature of the attractors (hidden or self-excited) that may exist. We apply numerical analysis techniques (2-parameter diagrams, bifurcation analysis, phase portraits, basins of attractions, etc) in accordance with the previous operating range in order to shed light on the plethora of competing dynamics of the model and possible forms of strange attractors as well. Another salient point of this work is the coexistence between five self-excited attractors (limit cycle and chaos) with a hidden attractor (limit cycle). We also examine the impact of symmetry breaking on the system response. An appropriate analog simulator of the coupled system is designed and simulated in PSpice in order to check the results reported during the theoretical analyses. We believe that the results of the present work complement and enrich previously published ones concerning the dynamics of a system composed of a van der pol oscillator coupled to a (non-oscillating) double-well oscillator.