A general construction method of a new high dimensional multi-wing nested hyperchaotic system

In engineering applications, low-dimensional chaotic systems often suffer from limited complexity and security vulnerability. To address this, a novel and general construction method for a new high-dimensional multi-wing chaotic system was proposed. In the new method, symbolic and periodic functions are nested to increase the dimensions of the system and realize the multi-wing effect of chaotic systems. Crucially, this method demonstrates remarkable generality and has been successfully applied not only to the new three-dimensional chaotic system introduced here but also to classical systems such as Lorenz and Chen. When the system dimension is increased to five or more, the multi-wing chaotic system exhibits hyperchaotic solid characteristics. Observing and analyzing the phase diagram, Lyapunov exponent, and the bifurcation diagram of the new and classical five-dimensional chaotic systems from multiple perspectives revealed that the high-dimensional chaotic system has the characteristics of large-scale parameter chaos. In addition, the shift enhancement and amplitude control of high-dimensional chaotic systems demonstrate that chaotic systems can change the polarity and amplitude of signals in practical applications. Finally, the circuit of a high-dimensional chaotic system is designed by introducing switches, and the simulation results are consistent with the numerical simulation results. Compared to their low-dimensional counterparts, generated high-dimensional multi-wing hyperchaotic systems offer significantly enhanced security performance owing to their increased complexity, higher entropy, and larger key space. These attributes, combined with the demonstrated controllability and hardware realizability, establish the practical value of the proposed method for secure communication and cryptographic applications.