Dynamical Analysis of Hyperbolic Sinusoidal Nonlinear Multi-Wing Chaotic Systems, Synchronization Methods and Analog Electronic Circuit Design

Chaotic systems contain nonlinear functions that have received much attention. This paper introduces a new four-dimensional chaotic system with multi-winged attractors, containing hyperbolic sinusoidal functions with unique quadratic curves that cause the attractors to change dramatically. When the single parameter is changed, single, double and quadruple wing chaotic attractors will be generated. The dynamical behavior of chaotic systems is analyzed and it is found that the system has coexistent attractors. Based on preparing the error system asymptotically stable at the origin, an adaptive control method is derived to achieve chaotic synchronization with unknown parameters. A new electronic circuit for chaotic systems is designed and implemented in FPGA hardware to illustrate the accuracy and validity of its existence.