Chaotic Dynamics by Some Quadratic Jerk Systems

Chaotic Dynamics by Some Quadratic Jerk Systems

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This paper is about the dynamical south shore axess desk evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a.By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored.The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos.

The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a cystorelin 100ml unique stable equilibrium) are also found via period-doubling cascades to chaos.A circuit implementation is presented for the hidden chaotic attractor.The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.