Nonlinear analysis, circuit implementation, and application in image encryption of a four-dimensional multi-scroll hyper-chaotic system

Abstract

This paper is based on the typical Sprott-C chaotic system and introduces a single-direction multi-scroll hyper-chaotic system with a scroll count of (2N + 2) by incorporating a multi-segment square function family. This innovation is the first key point of the paper, emphasizing the controllable scroll count compared to other single or double-scroll chaotic systems. Furthermore, by introducing additional state variables, the system achieves enhanced security and increased information capacity. The second key point highlights the rare occurrence of chaotic burst oscillations in the system’s time domain, distributed widely over a range of time, providing a significant innovation. The paper extensively validates the system’s dynamical behavior, including assessments of dissipation, equilibrium points, Lyapunov exponents, Poincaré sections, power spectra, and 0–1 tests, contributing to a deeper understanding of the system’s complexity. Subsequently, the paper further analyzes system characteristics regarding chaotic bursting oscillations, coexisting attractors, system complexity, and the impact of parameter variations. It underscores the system’s versatility and practicality through analog circuit design and FPGA (Field Programmable Gate Array) digital circuit design, confirming its feasibility and expanding its range of applications. Finally, the combination of the multi-scroll hyper-chaotic system with DNA (Deoxyribonucleic Acid) encryption algorithm is applied to image encryption. Through a comprehensive analysis of sensitivity in the key space, histograms, correlation, information entropy, robustness, and time efficiency of encrypted images, the paper verifies the feasibility and security of the encryption method, demonstrating promising prospects for future applications in the field of image encryption.