Study of bifurcations and chaos in the Muthuswamy–Chua system

• The dynamical behavior of an autonomous simplest electronic circuit had been studied.
• Under variation of two parameters we observed a rich variety of bifurcation phenomena.
• One and two-parameter bifurcation diagrams were studied.
• Route of period-doubling to chaos through different structures was observed.
• The theoretical results are compared with the available experimental results.

The dynamical behavior of an autonomous simplest electronic circuit that consists of three elements connected in series governed by three ordinary differential equations was investigated. The circuit elements are a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. Under variation of two parameters we observed a rich variety of bifurcation phenomena, including periodic, quasi-periodic, intermittent, and chaotic behaviors associated with this very simple nonlinear system. One and two-parameter bifurcation diagrams were studied. Route of period-doubling to chaos through different structures was observed. Our theoretical results are compared with the available experimental results and are found to be in good agreement with these results.