On the Dynamics of Chaotic Systems with Multiple Attractors: A Case Study

In this chapter, the dynamics of chaotic systems with multiple coexisting attractors is addressed using the well-known Newton–Leipnik system as prototype. In the parameters space, regions of multistability (where the system exhibits up to four disconnected attractors) are depicted by performing forward and backward bifurcation analysis of the model. Basins of attraction of various coexisting attractors are computed, showing complex basin boundaries. Owing to the fractal structure of basin boundaries, jumps between coexisting attractors are predicted in experiment. A suitable electrical circuit (i.e., analog simulator) is designed and used for the investigations. Results of theoretical analysis are verified by laboratory experimental measurements. In particular, the hysteretic behavior of the model is observed in experiment by monitoring a single control resistor. The approach followed in this chapter shows that by combining both numerical and experimental techniques, one can gain deep insight into the dynamics of chaotic systems exhibiting multiple attractor behavior.