A construction method for achieving tunable multi-wing complex chaotic system transformation from ‘dart-shaped’ to ‘circular’

To address the limitations of traditional untunable multi-wing chaotic systems in terms of stability and security, this study proposes a novel method for constructing a tunable multi-wing complex chaotic system. The proposed method is applied to investigate a three-dimensional self-excited chaotic system featuring two nonlinear terms. The key contributions of this work are threefold: First, the characteristics of the new three-dimensional chaotic system are analyzed, and its basic chaotic properties are proved. Second, a new method for constructing tunable multi-wing chaotic systems is proposed. By utilizing the rotational symmetry of the system, a chaotic attractor with an adjustable number of wings (2 n wings) is generated, enhancing the system’s adaptability and complexity. As n approaches infinity, the attractor trajectory converges to a circular shape, showcasing the system’s flexibility and application potential. Finally, the practicability of the system is verified through circuit simulation design using Multisim software and physical implementation on a breadboard. FPGA implementation is also discussed, highlighting the system’s potential in real-world applications. Overall, the methods and results presented in this paper contribute significantly to the exploration of complex dynamical systems and offer potential application value in secure communication, image encryption, and related fields.