Dynamical analysis, circuit implementation, and simultaneous application of a novel four-dimensional hyperchaotic system based on cosine functions

In this paper, based on the Jerk system, a novel four-dimensional hyperchaotic system containing five parametric constants, four variables, and a nonlinear term for a multi-vortex body is proposed. Based on the introduction of trigonometric functions, the basic dynamical properties of this four-dimensional hyperchaotic system, such as dissipation, equilibrium point, Lyapunov exponential spectrum, and bifurcation diagram, are investigated. Methods such as Poincare ' cross-section are investigated to verify the disorder and complexity of this hyper -chaotic system, and rich nonlinear dynamical phenomena such as immobile points, periodic orbits, multiplicative periodic orbits, chaotic oscillations, and hyperchaotic oscillations are analyzed and observed. Meanwhile, the simulation circuit of this hyperchaotic system is designed by Multisim software, and the chaotic circuit system is designed by FPGA to verify the realizability of the system. Finally, the synchronization controller corresponding to this hyperchaotic system is designed by coupling and tracking synchronization methods, and the tracking synchronization control time of the hyperchaotic system is optimized to lay the foundation for the application of the new chaotic circuit in a confidential communication.