A Novel Dynamical System: Chaos, Hidden Dynamics, Multistability, and Applications

Chaos is a significant concept in nonlinear dynamics, featuring numerous real-world examples and diverse applications, including cryptography. This study presents a novel chaotic system with a single fully unstable equilibrium point, where the equilibrium point is unstable in all directions — a property that is rare in chaotic systems, where the unstable equilibrium is typically a saddle. The dynamical properties of the proposed system are comprehensively analyzed through stability analysis, forward and backward bifurcation diagrams, Lyapunov exponent diagrams, and basin of attraction studies. Our analyses reveal that when the system’s equilibrium point is completely unstable, it generates monostable and multistable self-excited solutions, encompassing periodic and chaotic attractors. Conversely, in scenarios where the equilibrium point is stable, the system demonstrates periodic orbits, qualifying as hidden attractors. In the subsequent phase, we propose a sequential image encryption algorithm tailored for encrypting RGB images, utilizing the novel chaotic system as its foundation. The algorithm is rigorously evaluated using three prominent benchmark RGB images and subjected to various analyses and metric calculations, assuring its resilience against differential, statistical, and brute-force attacks.