Local Bifurcations with Coexisting Attractors and Offset Boosting in a Chaotic Jerk System

This study examines the local bifurcation of a chaotic Jerk system. The local stability of equilibrium points is analyzed and the occurrence of a pitchfork bifurcation at the origin is explored. For the proposed Jerk system, the occurrence of Hopf bifurcations at the origin is examined. Moreover, Lyapunov quantity techniques are employed to analyze the cyclicity of the system, demonstrating that four limit cycles can bifurcate from the origin. Finally, the coexistence of chaotic attractors is examined for two specific cases of the Jerk system using bifurcation diagrams, Lyapunov exponents and cross-sections. By applying offset boosting, the coexistence of multiple chaotic attractors is explored. All results presented in this study were obtained using MATLAB and Maple software.