The Dynamics of Local Bifurcation in a Novel Four-dimensional Hyperchaotic System

This paper reports the findings of a novel four-dimensional autonomous quadratic hyperchaotic system characterized by three nonlinear terms. This system is developed by introducing nonlinear state feedback into the second equation of the three-dimensional Yang chaotic system. A comprehensive dynamical study follows the presentation of the mathematical model. The study includes dissipation and symmetry, stability of equilibrium points, and dynamic behaviors such as the Lyapunov exponent spectrum, bifurcation diagram, Poincaré maps, and orbits. The Poincaré-Andronov-Hopf bifurcation theorem and center manifold theory are used in local bifurcation analysis to investigate pitchfork and Hopf bifurcation at zero equilibrium points. Numerical simulations have confirmed the mathematical discoveries.