The dynamic analysis, FPGA implementation, and adaptive synchronization control application of a multi‐vortex chaotic system based on nonlinear functions

In this paper, a three-dimensional Jerk chaotic system with saddle-focus equilibrium point and special rotational characteristics of attractors is proposed by constructing a three-dimensional chaotic system. Based on the three-dimensional Jerk chaotic system, a four-dimensional chaotic system based on the sign function and cosine function is proposed. Through detailed numerical simulations and theoretical analysis, we induce and control the emergence of multi-vortex structures in the system by adjusting system parameters, thereby influencing the overall dynamic characteristics of the system. The dynamical behavior of the system is analyzed using the 0–1 test, attractor coexistence, multiple bifurcations, two-parameter Lyapunov exponent, and complexity. It is found that the new four-dimensional chaotic system has the properties of multi-stability, transient chaos and offset enhancement. The circuit of this chaotic system was designed and simulated, and the digital circuit was implemented using field programmable gate array. The consistency between the simulation and implementation results proves the existence and feasibility of the system. Finally, based on the adaptive synchronization control algorithm, the system is applied to secure communication synchronization and the analysis confirms the superiority of the adaptive synchronization strategy, while enhancing the system’s ability to cope with external variations and demonstrating that it has a wide range of applications in various fields.