The effects of symmetry breaking on the dynamics of a simple autonomous jerk circuit

Abstract

We investigate the dynamics of a simple jerk circuit where the symmetry is broken by forcing a dc voltage. The analysis shows that with a zero forcing dc voltage, the system displays a perfect symmetry and develops rich dynamics including period doubling, merging crisis, hysteresis, and coexisting multiple (up to six) symmetric attractors. In the presence of a non-zero forcing dc voltage, several unusual and striking nonlinear phenomena occur such as coexisting bifurcation branches, hysteresis, asymmetric double scroll strange attractors, and multiple coexisting asymmetric attractors for some appropriate sets of system parameters. In the latter case, different combinations of attractors are depicted consisting for instance of two, three, four, or five disconnected periodic and chaotic attractors depending solely on the choice of initial conditions. The investigations are carried out by using standard nonlinear analysis tools such as Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase space trajectory plots. The theoretical results are checked experimentally and a very good agreement is found between theory and experiment.