Hidden multistability and quasi-conservative chaotic dynamics in a no-equilibrium modified Sprott system with application to image encryption

Abstract

This paper introduces a modified three-dimensional Sprott-type system without equilibrium points by combining a smooth hyperbolic-tangent feedback term with a quartic nonlinearity. The proposed model exhibits bounded multispiral chaotic dynamics, quasi-conservative behavior, and rich hidden multistability involving coexisting quasiperiodic and chaotic motions. Its nonlinear properties are investigated through equilibrium analysis, divergence, Lyapunov exponents, bifurcation diagrams, phase portraits, and Poincaré-based representations. The Lyapunov analysis is verified using the variational-equation method with periodic QR orthonormalization. As an application, six chaotic sequences generated by the system are incorporated into a two-round confusion–diffusion–permutation image-encryption framework with an image-dependent SHA-256 key update. The encryption performance is assessed through key sensitivity, histogram and correlation analyses, NIST statistical tests, differential measures, entropy, robustness, and computational cost. In addition, an analog circuit realization is examined through MultiSim simulations, supporting the practical feasibility of the proposed chaotic system.