An n-dimensional discrete attractor with sinusoidal waveform

Chaos is a rather unique phenomenon caused by nonlinear effects, with characteristics such as sensitivity to initial values, no periodicity, long-term unpredictability, fractal nature, and universality. Attractors are an important component in chaos theory. Different attractor shapes affect the complexity, periodicity and other properties of chaotic systems. This paper proposes a new n-dimensional discrete chaotic system construction scheme, which can generate chaotic attractors with sine wave shapes. In terms of system dynamics, the fixed point of the new system under different parameter values was analyzed. Taking 2-, 3-, and 4-dimensional discrete chaotic systems with sinusoidal waveforms as examples, phase space diagram analysis shows that they can indeed produce obvious sinusoidal wave attractors. Prove the irregularity of chaotic sequences through time series diagrams and spectrograms. Calculating the Lyapunov exponent in each dimension proves that the system is in a chaotic state. This paper also analyzes the chaotic state of the chaotic system under various parameter values through bifurcation diagrams, Lyapunov index diagrams, and demonstrates the relationship between the chaotic state of the system and the variation of the system parameters, and clarifies the parameter values of the system.