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. It is found that as the order q rises, the system transforms gradually from a dissipative system to a conservative system. Multiple coexisting attraction flows based on the Hamiltonian energy magnitude are present in this dual-property chaotic system. The complexity analysis shows that the system has a high level of complexity. NIST test indicates that the chaotic sequences produced by this dual-property chaotic system exhibit good pseudo-randomness. Finally, a Digital Signal Processing-based hardware platform confirms the physical realizability of the system.

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. In pursuit of heightened encryption speed, an FPGA-based chaotic sequence generator was developed for the image encryption algorithm, leveraging the proposed chaotic system. Furthermore, a more efficient scrambling algorithm was devised. Experimental results underscore the superior performance of this algorithm in terms of both encryption duration and 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. During the exploration, some special dynamical behaviors are analyzed in detail by using phase diagrams, bifurcation diagrams, Lyapunov exponential spectra, timing diagrams, and so on. After extensive simulation, several rare dynamical behaviors, including completely homogeneous, homogeneous, and heterogeneous initial offset boosting behaviors, are revealed. Among them, the initial offset boosting behaviors with identical phase trajectory structures have not been reported before, and the previously proposed homogeneous phase trajectories are locally different. By comparing with the integer-order system, two influence factors that affect the system to produce completely homogeneous and heterogeneous conservative flows are discovered. Eventually, the circuit is built on the digital signal processing (DSP) platform to demonstrate the physical realizability of the system. The experimental results are shown by the oscilloscope and agree with the theoretical analysis.

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. This means that small perturbations in the initial conditions in the mixing region will lead to the production of hidden extreme multistability. At the same time, these sieve-shaped basins are confirmed by the uncertainty exponent. Additionally, in the case of fixed parameters, when different initial values are chosen, the system exhibits a variety of coexisting transient transition behaviors. These 14 were also where the same state transition from period 18 to period 18 was first discovered. The above dynamical behavior is analyzed in detail through time-domain waveforms, phase diagrams, attraction basin, bifurcation diagrams, and Lyapunov exponent spectrum . Finally, the circuit implementation based on the digital signal processor verifies the numerical simulation and theoretical analysis.