Chaotic Oscillator with Diode–Inductor Nonlinear Bipole-Based Jerk Circuit: Dynamical Study and Synchronization

Abstract

This paper proposes a novel jerk circuit obtained by using an alternative nonlinear bipole component of inductor and diode in parallel. The circuit is described by five differential equations and investigated by the stability analysis, equilibria points, Kaplan–Yorke dimension, phase portraits, Lyapunov characteristic exponent estimation, bifurcation diagram and the 0–1 test chaos detection. The control parameter is adopted by varying the inductor [Formula: see text] value, this system can display periodic orbit, quasi-periodic orbit and chaotic behavior. The dynamic influence of transit diode capacitance is done and this confirms the robustness of the system to noise influence. The validity of the numerical simulations is experimentally realized through the phase portraits of the circuit. Finally, the synchronization of the systems is studied and time simulation results are presented.