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The spread of computer viruses represents a major challenge to digital security, underscoring the need for a deeper understanding of their propagation mechanisms. This study examines the stability and chaotic dynamics of a fractional discrete Susceptible-Infected (SI) model for computer viruses, incorporating commensurate and incommensurate types of fractional orders. Using the basic reproduction number R0, the derivation of stability conditions is followed by an investigation of how varying fractional orders affect the system’s behavior. To explore the system’s nonlinear chaotic behavior, the research of this study employs a suite of analytical tools, including the analysis of bifurcation diagrams, phase portraits, and the evaluation of the maximum Lyapunov exponent (MLE) for the study of chaos. The model’s complexity is confirmed through advanced complexity algorithms, including spectral entropy, approximate entropy, and the 0−1 test. These measures offer a more profound insight into the complex behavior of the system and the role of fractional order. Numerical simulations provide visual evidence of the distinct dynamics associated with commensurate and incommensurate fractional orders. These results provide insights into how fractional derivatives influence behaviors in cyberspace, which can be leveraged to design enhanced cybersecurity measures.

This paper describes a new fractional predator–prey discrete system of the Leslie type. In addition, the non-linear dynamics of the suggested model are examined within the framework of commensurate and non-commensurate orders, using different numerical techniques such as Lyapunov exponent, phase portraits, and bifurcation diagrams. These behaviours imply that the fractional predator–prey discrete system of Leslie type has rich and complex dynamical properties that are influenced by commensurate and incommensurate orders. Moreover, the sample entropy test is carried out to measure the complexity and validate the presence of chaos. Finally, nonlinear controllers are illustrated to stabilize and synchronize the proposed model.

Most of the papers published so far in literature have focused on the theoretical phenomena underlying the formation of chaos, rather than on the investigation of potential applications of chaos to the real world. This paper aims to bridge the gap between chaos theory and chaos applications by presenting a survey of very recent applications of chaos. In particular, the manuscript covers the last three years by describing different applications of chaos as reported in the literature published during the years 2018 to 2020, including the matter related to the symmetry properties of chaotic systems. The topics covered herein include applications of chaos to communications, to distributed sensing, to robotic motion, to bio-impedance modelling, to hardware implementation of encryption systems, to computing and to random number generation.

Computer viruses remain a persistent technological challenge in information security. They require mathematical frameworks that realistically capture their propagation in digital networks. Classical continuous-time, integer-order models often overlook two key aspects of cyber environments: their inherently discrete nature and the memory-dependent effects of networked interactions. In this work, we introduce a fractional-order discrete computer virus (FDCV) model, derived from a three-dimensional continuous integer-order formulation and reformulated into a two-dimensional fractional discrete framework. We analyze its rich dynamical behaviors under both commensurate and incommensurate fractional orders. Leveraging a comprehensive toolbox including bifurcation diagrams, Lyapunov spectra, phase portraits, the 0–1 test for chaos, spectral entropy, and C0 complexity measures, we demonstrate that the FDCV system exhibits persistent chaos and high dynamical complexity across broad parameter regimes. Our findings reveal that fractional-order discrete models not only enhance the dynamical richness compared to integer-order counterparts but also provide a more realistic representation of malware propagation. These insights advance the theoretical study of fractional discrete systems, supporting the development of potential technologies for cybersecurity modeling, detection, and prevention strategies.

The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and studies the dynamics of a Hopfield neural network (HNN) consisting of four neurons, where one of the synaptic weights of the neuron is replaced by a memristor. Theoretical aspects such as dissipation, the requirements for the existence of attractors, symmetry, equilibrium states and stability are studied. Numerical investigations of the model reveal that it develops very rich and diverse behaviors such as chaos, hyperchaos and transient chaos. These results obtained numerically are further supported by the results obtained from an electronic circuit of the system, constructed and simulated in PSpice. Both approaches show good agreement. In light of the findings from the numerical and experimental studies, it appears that the 4D Hopfield neural network under consideration in this work is more complex than its original version, which did not include a memristor.

Social media occupies an important place in people’s daily lives where users share various contents and topics such as thoughts, experiences, events and feelings. The massive use of social media has led to the generation of huge volumes of data. These data constitute a treasure trove, allowing the extraction of high volumes of relevant information particularly by involving deep learning techniques. Based on this context, various research studies have been carried out with the aim of studying the detection of mental disorders, notably depression and anxiety, through the analysis of data extracted from the Twitter platform. However, although these studies were able to achieve very satisfactory results, they nevertheless relied mainly on binary classification models by treating each mental disorder separately. Indeed, it would be better if we managed to develop systems capable of dealing with several mental disorders at the same time. To address this point, we propose a well-defined methodology involving the use of deep learning to develop effective multi-class models for detecting both depression and anxiety disorders through the analysis of tweets. The idea consists in testing a large number of deep learning models ranging from simple to hybrid variants to examine their strengths and weaknesses. Moreover, we involve the grid search technique to help find suitable values for the learning rate hyper-parameter due to its importance in training models. Our work is validated through several experiments and comparisons by considering various datasets and other binary classification models. The aim is to show the effectiveness of both the assumptions used to collect the data and the use of multi-class models rather than binary class models. Overall, the results obtained are satisfactory and very competitive compared to related works.

The Ueda oscillator is one of the most popular and studied nonlinear oscillators. Whenever subjected to external periodic excitation, it exhibits a fascinating array of nonlinear behaviors, including chaos. This research introduces a novel fractional discrete Ueda system based on Y-th Caputo fractional difference and thoroughly investigates its chaotic dynamics via commensurate and incommensurate orders. Applying numerical methods like maximum Lyapunov exponent spectra, bifurcation plots, and phase plane. We demonstrate the emergence of chaotic attractors influenced by fractional orders and system parameters. Advanced complexity measures, including approximation entropy (ApEn) and C0 complexity, are applied to validate and measure the nonlinear and chaotic nature of the system; the results indicate a high level of complexity. Furthermore, we propose a control scheme to stabilize and synchronize the introduced Ueda map, ensuring the convergence of trajectories to desired states. MATLAB R2024a simulations are employed to confirm the theoretical findings, highlighting the robustness of our results and paving the way for future works.

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.

The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach.

In recent years, there has been a marked surge in research focused on nonlinear oscillators. Among these, a particular emphasis has been placed on a class of oscillators distinguished by their concealed attractors, drawing considerable attention due to their unique characteristics. This paper delves into the exploration of an elegant oscillator belonging to this distinctive class. Despite comprising five terms and lacking equilibrium points, this oscillator displays remarkably intricate dynamics. The study covers various aspects such as chaos, hidden attractors, offset boosting, and notably, different strange attractors exhibited by this oscillator. Additionally, approaches involving synchronization for such oscillators are introduced. Apart from the presentation of the novel chaotic oscillator, the synchronization of a nominal and uncertain chaotic system is evinced by the sliding mode technique (super‐twisting algorithm) in the first case, and a robust controller is synthesized, respectively. The appropriate Lyapunov functions are implemented in the two synchronization strategies leading to obtain suitable control strategies to achieve fast and accurate control laws. The respective simulations are performed along with the conclusions of this work.