Search Results (211)

This study investigates the nanomechanical response of aluminum substrates coated with crystalline or amorphous equiatomic FeNiCrCo compositionally complex alloy (CCA) layers using molecular dynamics nanoindentation. We evaluated the influence of coating microstructure and pre-relaxation via Monte Carlo/molecular dynamics (MC/MD) on deformation behavior at shallow (35 Å) and deep (65 Å) indentation depths. The relaxation process is critical for equilibrating internal stresses and homogenizing the initial stress field in amorphous phases, while preventing chaotic defect multiplication in crystalline lattices, yet it simultaneously promotes Fe and Cr surface segregation consistent with the equilibrium chemical short-range ordering of the alloy. The results reveal distinct deformation mechanisms: crystalline coatings exhibit higher peak indentation forces of about 300 ± 16 eV/Å characterized by discrete force fluctuations indicative of localized plastic events, while amorphous coatings show lower peak loads (~170–220 ± 12 eV/Å), corresponding to a reduction in load-bearing capacity of roughly 25%–40%, and smooth, continuous deformation governed by shear transformation zones. Notably, in amorphous systems, pressure-induced local crystallization occurs under load, with ordered FCC/HCP regions persisting after unloading, indicating partial irreversibility of the phase transition. Upon deep indentation into the substrate, the amorphous system exhibits a sharp increase in stiffness due to substrate compaction, whereas the crystalline system maintains high load-bearing capacity with reduced defect density in the relaxed state compared to the non-relaxed counterpart. Relaxation significantly reduces force-curve fluctuations in both systems, enhancing the stability of the mechanical response. Compared with uncoated aluminum, which exhibits extensive twin propagation and deep defect penetration, the FeNiCrCo-coated systems approximately halve the defect penetration depth and reduce the defective-atom volume fraction in the substrate by about a factor of two, thereby more effectively confining plastic deformation and preserving substrate integrity under the simulated conditions. These findings demonstrate that the synergy between coating crystallinity and rigorous relaxation protocols governs stress distribution patterns—localized hotspots in amorphous phases versus extended networks in crystalline ones—providing key insights for designing advanced protective coating–substrate systems with optimized mechanical performance. Full article

To address the limitations of existing chaotic systems such as complex structure and potential chaotic degradation, this paper proposes a novel four-dimensional discrete chaotic system (4D-DCS) and an image encryption algorithm based on it. The 4D-DCS is constructed by integrating a feedback controller and modulo operation into a linear discrete-time system, featuring a simple structure without the need for intricate matrix reconstruction or memristor circuits. Mathematical analysis confirms its chaos in the sense of Li–Yorke and numerical simulations including Lyapunov exponent (LE) analysis, 0–1 test, and NIST SP 800-22 test demonstrate its hyperchaotic characteristics and excellent pseudorandomness. Based on the 4D-DCS, the proposed encryption algorithm employs SHA-256 to generate initial states for key uniqueness, combines row–column permutation to disrupt pixel correlation, and adopts a reversible neural network for diffusion to enhance confusion capability. Comprehensive security analysis shows that the algorithm achieves an NPCR of ∼99.61% and a UACI of ∼33.46%, a key space of $2^{216}$, information entropy close to 8, and correlation coefficients of encrypted images near 0. It also exhibits strong robustness against differential, cropping, noise, and chosen-plaintext attacks. Comparative analysis with state-of-the-art algorithms validates the 4D-DCS’s advantages in structural simplicity and stability, and the encryption algorithm’s superiority in security and practicality, making it suitable for security-critical applications such as image encryption. Full article

Stick–slip vibration, reversal, axial impact, and dynamic instability are major challenges in deep drilling operations and are closely associated with nonlinear bit–rock interaction. To investigate these phenomena, this study develops a nonlinear axial–torsional coupled dynamic model of a drill-string system by integrating rock surface morphology evolution with a Stribeck dry friction model. The drill string is discretized into a distributed lumped-parameter model with coupled axial and torsional degrees of freedom. A surface morphology matrix is introduced to simulate the rock-cutting process, while the Stribeck friction model is employed to characterise the nonlinear frictional behaviour at the bit–rock interface. Time-domain simulations, bifurcation analysis, and frequency spectrum analysis are performed to investigate the dynamic responses of the system. The results indicate that rock surface morphology evolution significantly influences the contact conditions and frictional behaviour at the bit–rock interface, and together with dry friction induces transitions among steady-state, multi-periodic, and chaotic motions. Stick–slip vibration is accompanied by axial impact, bit bounce, and a reduction in the dominant torsional vibration frequency. In addition, variations in both driving and frictional parameters can trigger dynamic instability and state transitions. The proposed model provides an effective framework for analysing nonlinear drilling dynamics and offers theoretical guidance for drill-string vibration suppression, drilling parameter optimisation, and efficient drilling in complex formations. Full article

This study examines a discrete fractional-order predator–prey system incorporating a Holling type-III functional response. The Caputo fractional derivative is employed because it naturally incorporates memory and hereditary effects while preserving biologically meaningful initial conditions. The system is formulated from a biologically relevant continuous fractional-order framework through the application of the piecewise constant argument approach, enabling an analysis of how memory-dependent effects and discrete dynamics influence predator–prey interactions. The existence and local stability of fixed points are determined by using the Jacobian matrix and eigenvalue conditions. The bifurcation of the positive fixed point is analyzed by using the center manifold and normal form methods. Numerical simulations, including bifurcation diagrams, phase portraits, and maximum Lyapunov exponent plots, confirm our analytical results and reveal periodic, quasiperiodic, and chaotic behavior. The findings of this study reveal that the combined influence of memory-dependent dynamics, nonlinear predator–prey interactions, and discrete-time effects can generate rich and complicated behaviors in fractional-order predator-prey systems. Full article

The large-scale integration of distributed photovoltaics (DPVs) into the distribution network exacerbates voltage fluctuations and substantially increases network losses. To improve the voltage quality and economic efficiency of distribution networks, a Volt/Var optimization (VVO) model is established. Coordinating multiple heterogeneous devices, the model aims to minimize the total voltage deviation, the total network losses, and the regulation cost of discrete equipment simultaneously. Considering multi-constraint coupling characteristics, a quantitative method is proposed to evaluate the reactive power regulation potential of DPVs under intricate operating conditions. Then, the multi-strategy integrated rime optimization algorithm (MSIRIME) is utilized for the model solution. Fuch chaotic mapping generates uniformly distributed and ergodic initial populations. A dual-branch search mechanism combining the snow ablation optimizer with the rime optimization significantly enhances global exploration capabilities. The guided learning strategy balances exploration and exploitation for high-dimensional VVO, preventing local optima. Case tests on a modified IEEE 33-bus system demonstrate that the proposed model exhibits excellent effectiveness and robustness. Moreover, MSIRIME exhibits better optimization performance than some classic and recently proposed strategies, reducing the average network losses and voltage deviation over 30 independent runs by at least 5.87% and 52.22%, respectively, relative to those of the compared methods. Full article

The paper presents a comparative analysis of the Differential Transform Method (DTM) with respect to classical numerical approaches, such as the Euler and Runge–Kutta methods, using the nonlinear Duffing equation as a representative example. This equation, being a prototypical model of dynamical systems exhibiting chaotic behavior, provides a demanding test environment for techniques used to approximate solutions of ordinary differential equations. The aim of the study is to assess the accuracy, stability, and computational efficiency of the considered methods as functions of the system parameters. The DTM approach, based on differential transform and a series representation of the solution, was compared with classical discretization schemes. In the DTM framework, the symmetry of the system is not imposed explicitly, but emerges from the initial conditions and the recursive structure used to determine the series coefficients. However, the preservation of this symmetry may be disrupted, leading to asymmetry due to truncation of the series expansion and the propagation of numerical errors. The obtained results indicate that DTM can serve as a competitive alternative to conventional methods, particularly in short-term simulations of nonlinear dynamical systems, offering high accuracy at a relatively low computational cost. Full article

This paper investigates a discrete diffusion carbon emission-absorption model with periodic boundary conditions derived via the piecewise constant argument scheme. The existence of equilibrium points is established, and sufficient conditions for the local asymptotic stability of the positive equilibrium are derived through eigenvalue analysis. Then, uniform boundedness of positive solutions is proved, and the global asymptotic stability of the interior equilibrium is established by an iterative method and the comparison principle for difference equations. Furthermore, the model is shown to undergo a flip bifurcation when a critical parameter threshold is reached, leading to period-doubling dynamics and chaotic behavior. The influence of spatial diffusion is examined through a Turing instability analysis, yielding conditions for diffusion-driven instability and spatial pattern formation. Finally, Decision Tree and Random Forest classifiers are used as proof-of-concept tools to efficiently approximate the analytically derived stability regions using Monte Carlo-generated data. Both classifiers successfully reproduce the analytical stability structure, while the Random Forest classifier provides higher accuracy and smoother stability boundaries. Numerical simulations support the theoretical results and illustrate the stability and bifurcation phenomena exhibited by the model. These findings indicate that the proposed framework is useful for analyzing carbon emission-absorption dynamics and that machine learning can serve as an efficient computational surrogate for identifying stability regions in nonlinear dynamical systems. Full article

Memtransistors, as multi-terminal devices with gate-tunable memristive behavior, offer new opportunities for nonlinear circuit design beyond conventional two-terminal memristors. The paper proposes a novel four-dimensional chaotic oscillator by integrating a three-terminal memtransistor model with a memristor. The mathematical models of both devices are established, and their equivalent circuits are presented. Based on the memtransistor model, a chaotic circuit is constructed, and its dynamical behavior is investigated by the Lyapunov exponent spectrum, bifurcation diagram, dynamical map, and other tools. It is found that the chaotic circuit has complex nonlinear characteristics and that the phenomenon of attractor coexistence exists. Furthermore, the chaotic system is discretized by the Euler approach, and experiments on an STM32-based circuit confirm the reliability of the theoretical analysis. This work provides a hardware-validated platform for studying memtransistor-based nonlinear circuits and may find applications in chaos-based secure communication and neuromorphic computing. Full article

In this study, we present a discrete switching host–parasitoid model that incorporates biological and chemical control interventions within the integrated pest management (IPM) measures. The coupling of multi-tactic control measures induces rich and complex dynamical behaviors in the proposed system. We begin by systematically characterizing the existence and stability of fixed points in the control subsystem. The analysis then proceeds to demonstrate how the system undergoes multiple bifurcation routes, including period-doubling, transcritical, and Neimark–Sacker bifurcations. Building on this theoretical foundation, extensive numerical simulations are conducted, not only corroborating our analytical predictions but also revealing emergent phenomena such as cascading period-doubling routes and chaotic regimes. Finally, high-resolution two-parameter stability diagrams are employed to identify the critical dynamical transition boundaries, and the corresponding ecological implications for practical pest management decision-making are elaborated in depth. Full article

At present, constructing discrete chaotic systems with unique characteristics and chaos has become a focal topic in the field of nonlinear research. This paper presents a new framework for designing multi-cavity chaotic maps in polar coordinates. It constructs the basic chaotic map through nonlinear curves (such as Lotus curve, rose curves, and star curves) and generates multi-cavity attractors based on modular arithmetic. The nonlinear curves introduce complex deformations in the angular and radial components, while modular arithmetic serves as a folding mechanism to confine the dynamics to a specific range. The combined effect of these two elements forms multiple clearly separated chaotic cavities in the phase space. The number, size, shape, and chaotic characteristics of the cavities can be flexibly controlled by parameters. However, the introduction of fractional-order difference operators will disrupt the multi-chamber structure and make the system more complex. Furthermore, a data-hiding scheme based on the cavities is developed: the cavities act as natural isolation containers to embed information bits, and the chaotic dynamics provide encryption and confusion mechanisms. Experiments show that the designed chaotic map has high complexity and rich bifurcation behaviors; the data-hiding scheme performs well in terms of embedding capacity and security. Full article

Understanding how information spreads in complex networks is essential for analyzing social influence, opinion formation, and the emergence of collective behavior. In many real-world systems, interactions are not instantaneous but involve delays due to communication, cognition, and response times. Motivated by this observation, the present paper investigates a delayed network model of information spreading, focusing on how time delay and interaction strength shape the system’s dynamical behavior. The novelty of the proposed approach lies in the formulation of a discrete-time network model that explicitly incorporates delayed interactions within a nonlinear dynamical framework. Using delay difference equations, the model captures both local coupling effects and memory-driven feedback, allowing for a systematic study of their combined impact on stability and complexity. Analytical results establish the existence of steady states and provide conditions for their local stability, revealing critical thresholds at which the system undergoes qualitative transitions. These findings are complemented by extensive numerical simulations. In particular, bifurcation analysis and the computation of the largest Lyapunov exponent demonstrate a progression from stable equilibria to oscillatory behavior, and further to chaotic dynamics as the delay and coupling strength increase. Our results highlight the fundamental role of delay as a mechanism that enhances nonlinear complexity and promotes unpredictable dynamics in networked systems. These insights contribute to a deeper understanding of information propagation processes, and may inform the design and control of spreading phenomena in social and technological networks. Full article

Cycle-to-cycle variability of switching parameters inherent to memristive devices introduces significant problems in the design of neuromorphic systems and non-volatile memory. This study investigates the dynamics of a second-order memristive system incorporating capacitive effects that model parasitic charge within individual memristors, addressing both the technical need for accurate analysis of complex regimes and the demand for exploratory environments. Simulations were performed using CUDAynamics, an interactive software suite developed by the authors, which utilizes parallel computing, primarily via NVIDIA Compute Unified Device Architecture (CUDA). It integrates multiple analysis tools for dynamical systems, including bifurcation diagrams, the largest Lyapunov exponent and periodicity mapping, and interactive navigation in multidimensional parameter spaces. The memristive system was discretized applying multiple integration methods with a fixed time step and various waveforms of the input signal. Analysis tools revealed well-defined regions of chaotic dynamics in the memristor resistance parameter space as functions of input signal properties. Sinusoidal and triangular waveforms produced topologically similar distributions of dynamical regimes, whereas the square waveform, mimicking digital inputs, generated distinct dynamical patterns while still preserving chaotic trajectories under specific conditions. Interactive visualization capabilities of CUDAynamics effectively demonstrate attractor evolution and hysteresis deformation, providing immediate visual feedback that significantly enhances conceptual comprehension of nonlinear feedback mechanisms. Beyond its practical implications for the design of analog and digital memristive devices, CUDAynamics offers a scalable, open-source toolkit to aid researchers and engineers in exploring complex dynamical phenomena. Full article

Ultrafast physical random bit generators (PRBGs) are essential components for modern applications in secure communication, quantum cryptography, encrypted optical fiber sensing and artificial intelligence. While optical chaos-based PRBGs offer high-speed capabilities, conventional systems often rely on discrete components that suffer from system complexity and environmental instability. This paper proposes and experimentally demonstrates a robust, integrated solution using a two-section mutual injection DFB laser. The device was fabricated using the reconstruction equivalent chirp (REC) technique, which provides precise control over grating phase variation while utilizing low-cost, high-volume fabrication methods. The laser sections, each measuring 450 μm in length, were designed with a free-running wavelength difference of 0.3 nm to ensure a flat optical spectrum and enhanced chaotic dynamics. By optimizing the bias currents, we achieved a chaos RF bandwidth of 20.1 GHz. Notably, the resulting chaotic signal lacks time-delayed signatures, which simplifies the randomness extraction process. To generate random bits, the chaotic waveform was sampled by an 8-bit analog-to-digital converter at 100 GSa/s. Following post-processing through delay-subtracting and the extraction of the four least significant bits (4-LSBs), we realized a total physical random bit rate of 400 Gb/s. The randomness of the generated sequence was successfully verified using the NIST SP 800-22 statistical test suite. This approach offers a compact, energy-efficient, and high-performance integrated chaotic source suitable for secure communication and high-performance computation. Full article

The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions is an ergodic finite difference operator with an exponentially decaying spectral projection, then the large-block form of the entanglement entropy is the so-called area law. However, the only class of one-body Hamiltonians for which this spectral condition was verified consists of discrete Schrödinger operators with random potential. In this paper, we prove the area law for several classes of Schrödinger operators whose potentials are ergodic but not random. We begin with quasiperiodic and limit-periodic operators and then move to a highly non-trivial case of potentials generated by subshifts of finite type. These arose in the theory of dynamical systems when studying chaotic phenomena. The corresponding asymptotic study requires involved spectral analysis, which therefore constitutes the bulk of the paper. Specifically, we prove uniform localisation of the eigenfunctions for the Maryland model and exponential decay of the eigenfunction correlator for various models. We believe these properties are of significant independent interest. Full article

This paper investigates a discrete-time fractional-order predator–prey model incorporating a double Allee effect in the prey population, derived from a fractional differential system via the piecewise constant argument method to capture both memory effects and density-dependent constraints. We establish the existence and local stability of all biologically meaningful equilibria and show that the interaction between fractional memory and the double Allee threshold significantly influences the stability of the coexistence state. Through the integration of linear stability analysis and center manifold reduction, we are able to obtain explicit conditions for Neimark–Sacker and period-doubling bifurcations. The system exhibits rich dynamics, including periodic oscillations, quasi-periodicity, and chaos. The double Allee effect plays a key role in shaping system stability. To suppress instability and chaotic behavior, feedback and hybrid control strategies are applied and shown to be effective. Numerical simulations are given to confirm the results obtained by the theoretical analysis and to show the transitions among different dynamical states, in which the fractional-order memory and multiple Allee effects play important roles. Full article