Theoretical study and circuit implementation of three chain-coupled self-driven Duffing oscillators.

Abstract

In this paper, we describe the scenario from the birth of oscillations to multi-spiral chaos in a novel system composed of three chain-coupled self-driven Duffing oscillators. Eight of the equilibrium points develop (multiple) Hopf bifurcation when varying a parameter (e.g., coupling coefficient). Considering the computer integration of the state equations, the combined exploitation of Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase portraits, unusual and attractive features were highlighted including the coexistence of eight bifurcation branches, Hopf bifurcations, a multitude of coexisting types of oscillations and a six-spiral chaotic attractor, just to cite a few. Using basic electronic components, the electronic circuit of the three chain-coupled Duffing oscillator system is performed. Orcad-PSpice simulated dynamics of the proposed chain-coupled analog circuit confirm the theoretically disclosed features. Moreover, the practical feasibility of the coupled system is demonstrated by considering microcontroller-based hardware realization.