Dynamical analysis and bifurcation mechanism of four-dimensional hyperchaotic system

Chaos generation depends on nonlinear elements and nonlinear terms in systems of ordinary differential equations. The design and investigation of simple autonomous hyperchaotic systems are of great significance in theoretical interest. This paper presents a novel four-dimensional dissipative hyperchaotic system with only two nonlinear terms. The complex dynamical behaviors of the system are demonstrated with phase portraits, Lyapunov exponents spectrum, bifurcation diagram, Poincaré map and Kaplan–Yorke dimension. Again, the numerical simulation results indicate that the polarity of chaotic signals is transformed flexibly by the offset boosting. Particularly, a symmetric periodic bursting oscillation and bifurcation mechanism are revealed. The bifurcation conditions of periodic bursting are studied in detail by constructing the fold and Hopf bifurcation set of fast-scale systems. The proposed system exhibits symmetric periodic fold/Hopf bursting oscillations with the change of parameters. Finally, hardware experiments verify the theoretical analysis and numerical simulation of the periodic bursting. Its potential value in engineering applications is further demonstrated.