Kehui Sun

Many dynamical systems operate in disordered environments. In this Letter, we investigate how quenched randomness modifies particle diffusion. We show that, in finite-strength potential landscapes, low disorder densities can induce logarithmically ultraslow diffusion. The underlying mechanism originates from local symmetry breaking in particular potential configurations: Barrier-well structures form directional channels, causing particles to undergo hierarchical capture, escape, and recapture processes. A coarse-grained channel theory yields an approximate scaling prediction for the mean-square displacement. Counterintuitively, when the disorder density reaches the fully disordered limit, the system returns to normal diffusion, revealing a nontrivial, nonmonotonic relationship between disorder density and transport type. This mechanism is observed in both nonlinear maps and stochastic systems.

To ensure high-security levels in secure communication, we propose a Fractional-Order Memristor (FOM) chaotic system with a complex nonlinear term combined with an absolute value function. Using the Adomian Decomposition Method, we decompose and analyze the FOM system of the nonlinear term and differential equations. The dynamics of the system is analyzed by using Lyapunov exponents, bifurcation diagrams, basin attractors, complexity analysis, and phase diagrams. The results demonstrate that the proposed system exhibits rich nonlinear dynamics, high complexity, and persistent chaotic behavior over a broad range of the fractional-order q. In addition, we investigate the synchronization between the FOM chaotic systems and a hidden attractor. Finally, an analog circuit of the FOM system is implemented, demonstrating that the phase diagrams obtained are consistent with that of the simulation analysis.

Existing research on locally active memristors (LAMs) has primarily focused on first-order systems. Compared to classical first-order models, the core advantage of second-order memristors lies in the introduction of a second internal state variable, which enables more complex dynamical behavior and information processing capabilities than first-order memristors. This paper proposes a discrete second-order LAM (DSLAM). By coupling this novel memristor with a one-dimensional sine map, a three-dimensional chaotic map is constructed. Analysis of the Lyapunov exponent spectra and bifurcation diagrams confirms that this map exhibits enhanced chaotic properties compared with a two-dimensional chaotic map based on a discrete first-order LAM (DFLAM). Further dynamical analysis reveals that the new DSLAM chaotic map exhibits rich dynamical properties, high complexity, multiple coexisting attractors, and sensitivity to initial conditions. To validate the feasibility of DSLAM circuit implementation, a PSIM-based simulation circuit is designed, and a DSP-based digital hardware implementation is developed. The DSLAM proposed in this paper offers a new approach for extending LAMs to the second-order memristor, demonstrating improved dynamical characteristics and providing an effective pathway for DSLAM research.

Extreme multistable chaotic systems, capable of generating signals with diverse amplitudes, offer significant advantages for secure communications. However, making any 3-D quadratic continuous chaotic system exhibit extreme multistability without increasing the system’s dimensionality or complexity remains a challenging task. To address this issue, this paper proposes a novel design method, termed the Generalized Equilibrium Point Expansion Method (GEPEM). GEPEM is governed by three design criteria: trigonometric substitution, equilibrium solvability preservation, and chaos control. GEPEM offers the advantages of broad generality and strong model generalization, without requiring additional state variables. We apply GEPEM to the unified chaotic system and the Sprott B system, and numerical simulations demonstrate an infinite number of coexisting double-wing attractors along various spatial axes. Furthermore, coexisting self-oscillating, time-dependent multiwing attractors are observed. To verify the feasibility and engineering practicality of GEPEM, we conduct circuit simulations and develop a DSP-based platform. Finally, we design a PRNG based on the multistable chaotic system. With all P-values exceeding the 0.01 threshold in the NIST SP 800-22 tests, the designed PRNG exhibits excellent randomness.

To enhance the structural complexity of multi-cavity chaotic maps, a new complex exponential chaotic map (CECM) is proposed based on complex exponential functions. Its attractor shape is sensitive to parameters. By integrating the CECM with step functions, a heterogeneous multi-cavity hyperchaotic map (HMCM) is created that generates multiple cavities with unique structures, enhancing system complexity. Dynamical analyses, including attractor phase diagram, Lyapunov exponents, and permutation entropy complexity, verify the hyperchaotic performance across a wide parameter range. The HMCM is implemented on a digital signal processor platform, performing on-chip computations of the bifurcation diagram and Lyapunov exponents. The integrated hardware analysis confirms the physical feasibility, robust chaos, and low-resource usage of the map.