Design of a New Chaotic System by a Non–Smooth Controller and its Application

Chaos theory constitutes a fundamental discipline within nonlinear science. Chaotic systems, leveraging their sensitive dependence on initial conditions, have found extensive applications in information security. While numerous chaotic systems have been developed via continuous control methodologies in recent years, the design of such systems under non-smooth control regimes remains challenging due to the lack of systematic theoretical frameworks. Under what conditions can non-smooth control schemes induce deterministic chaos in nonlinear systems? What systematic methodology enables the construction of non-smooth controllers that guarantee chaotic dynamics generation while maintaining system stabilizability? Building upon the principles of chaos theory, this study introduces a novel chaotic system developed via a non-smooth control design methodology. The newly developed chaotic system is analyzed through its complex attractors and equilibrium points. Additionally, an image encryption algorithm based on this system is investigated, combining block scrambling and diffusion techniques in its design. The feasibility of the proposed encryption algorithm is validated through numerical simulations, demonstrating an expansive key space and robust security characteristics as evidenced by comprehensive security analyses.