Dynamics analysis of a novel parametrically controllable symmetric multi-scroll chaotic system and FPGA design of an image encryption system

This paper proposes a novel parameter-controllable symmetric multi-scroll chaotic system, which exhibits more complex and rich dynamic behavior compared to traditional multi-scroll chaotic systems. Additionally, its simple mathematical model is better suited for hardware implementation, making it highly promising for secure communication applications such as image encryption. By adjusting the control parameter u, the number and distribution of symmetric scrolls can be varied, allowing for effective regulation of the system’s energy stability. Numerical simulations have been conducted to analyze the dynamic performance of the proposed system, focusing on Lyapunov exponents, bifurcation characteristics, equilibrium points, and fractal dimensions, which collectively confirm the complexity of the system’s output sequences. Moreover, the system displays unique dynamic phenomena, including special multistability in both energy-conserving and dissipative scenarios, as well as distinctive offset behavior and transient self-similarity. To enable efficient implementation on field-programmable gate arrays (FPGA), we propose a generic trigonometric function mapping algorithm model designed for rapid hardware computation of trigonometric functions, capable of completing calculations within a single clock cycle. This model also allows for flexible precision selection to balance resource costs and performance according to specific requirements. Finally, the modular design of the proposed system and its hardware implementation for image encryption have been successfully realized on a Xilinx FPGA. The novel symmetric multi-scroll chaotic system demonstrates high sensitivity to initial conditions and exhibits rich and unique dynamic behaviors. In practical image encryption applications, this method offers excellent encryption performance, underscoring its significant potential for secure communication research. •The novel mathematical model of chaotic systems is simple and rich in dynamic properties.•Controllable number of symmetric scrolls and distribution range parameters with adjustable energy stability.•The output sequences of the system has good complexity and pseudo-randomness.•Flexible, general-purpose FPGA trigonometric algorithm model for fast trigonometric operations.•Implementing chaos and image encryption systems into hardware demonstrates the practical value of the research.