A new four-dimensional chaotic system with rich transitional characteristics between dissipative and conservative.

The general form of the Hamiltonian function serves as the foundation for the creation of a new four-dimensional chaotic system in this study. We discover that the external excitation parameter d, the internal parameter a, and all initial values have a transforming influence on the system property. Additionally, the corresponding fractional-order chaotic system in accordance with the constructed four-dimensional chaotic system is proposed.

Adaptive Fast Image Encryption Algorithm Based on Three-Dimensional Chaotic System.

This paper introduces a novel three-dimensional chaotic system that exhibits diverse dynamic behaviors as parameters vary, including phase trajectory offset behaviors and expansion-contraction phenomena. This model encompasses a broad chaotic range and proves suitable for integration within image encryption. Building upon this chaotic system, the study devised a fast image encryption algorithm with an adaptive mechanism, capable of autonomously determining optimal encryption strategies to enhance algorithm security.

Study of a novel conservative chaotic system with special initial offset boosting behaviors.

Conservative systems are increasingly being studied, while little research on fractional-order conservative systems has been reported. In this paper, a novel five-dimensional conservative chaotic system is proposed and solved in a fractional-order form using the Adomian decomposition method. This system is dissipative in the phase volume, but the sum of all Lyapunov exponents is zero.

A novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions.

Based on the pure mathematical model of the memristor, this paper proposes a novel memristor-based chaotic system without equilibrium points. By selecting different parameters and initial conditions, the system shows extremely diverse forms of winglike attractors, such as period-1 to period-12 wings, chaotic single-wing, and chaotic double-wing attractors. It was found that the attractor basins with three different sets of parameters are interwoven in a complex manner within the relatively large (but not the entire) initial phase plane.