In this paper, novel control techniques are presented for stabilization and synchronization of Hopfield neural networks by the fast terminal sliding mode controller in the first case and projective synchronization in the second case. To summarize the main contributions and innovations presented in this research paper, the following issues are considered as part of the innovations. First, a novel chaotic Hopfield network is discovered. Second, the projective stabilization and synchronization by terminal sliding mode control is provided. This study begins with the dynamic analysis of the chaotic neural networks. This consists of the stability and bifurcation of a single neuron or node of the network and in the case of the stability analysis, the respective Lyapunov stability of the whole chaotic neural networks. Then, the stabilization of the neural network is performed by a terminal sliding mode controller FTSMC which is designed by the implementation of a Lyapunov functional. The closed-loop stability and fast convergence to the sliding phase is achieved by means of the FTSMC, improving other results found in the literature. Then, a projective synchronization controller is designed in order to achieve an accurate synchronization between the drive and response chaotic system. Finally, a numerical example is provided to ensure and validate the theoretical results obtained in this research study. Conclusions and discussions are provided in the end of this paper.

The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains challenging due to the multifaceted influence of coupling topology, interaction strength, and oscillator frequency detuning. Despite extensive theoretical investigations over the decades, numerous aspects remain unexplored, particularly those that bridge theoretical predictions with experimental observations-an essential step towards deepening our understanding of real-world dynamical phenomena. This work investigates the complex dynamics of unidirectionally coupled nonisochronous Stuart-Landau oscillators. Calculations of steady-states and their stability analysis further reveal that periodic attractors corresponding to weak forcing or coupling regimes are dynamically unstable, which pushes the system towards quasiperiodic oscillation on the torus attractor. The connection between amplitudes in the synchronized state and the isola bifurcation is established. The mapping of parameter values with the kind of attractor of the oscillatory system is presented and classified into periodic, quasiperiodic, partially synchronized, and chaotic regions. The results of this study can be leveraged to design complex yet controllable dynamical architectures.

Unsustainable exploitation of environmental resources can destabilize ecosystems, increasing the risk of sudden collapse of common resource pools through regime shifts. This sudden collapse of common resources, also known as the tragedy of the commons, is a fundamental problem in game theory. In this study, we adopt an eco-evolutionary game-theoretic framework to study the dynamics of a coupled human-environment system with a renewable resource considering six distinct game combinations. The resource follows logistic growth with an Allee effect and is subject to a Holling type-I functional response. In particular, we focus on how variations in harvesting effort lead to the emergence of the tragedy of the commons through regime shifts. Our results unveil a rich spectrum of bifurcation mechanisms that can drive regime shifts. We further confirm that resource abundance is governed by both intrinsic ecological dynamics and emergent human behavior, with adaptive strategies and suitable incentives playing a key role in sustaining the system despite the presence of defectors. Furthermore, variations in system parameters can modulate the timing of environmental collapse, either delaying or accelerating its onset as the harvesting effort of defectors increases.

Biological neurons can perceive a variety of physical and chemical signals and appropriate firing modes can be induced to maintain suitable energy levels accompanying with right firing patterns. Physical and chemical stimuli including current, electromagnetic field, acoustic wave, illumination, and odor can be converted into equivalent currents on the cell membrane or ion channels. Memristive terms enable the sensor ability of electromagnetic induction in biophysical neurons by introducing memristive current and variables including charge and magnetic flux. The activation of memristive synapses can enhance the controllability and multistability of memristive neurons, and then energy diversity supports adaptive control in intrinsic parameters and mode selection in neural activities. These functional neurons can be clustered to develop functional neural networks and gradient energy diversity and local energy balance support formation of defects and heterogeneity, which control the wave propagation and synchronization stability of neural networks. This special issue summarizes new achievements about physical descriptions in functional biophysical neurons and networks, and functional enhancement of neuron models and neural circuits, wave propagation in neural networks. This SI has collected 67 papers, and these results in this special issue have potential application in control of electromechanical arms and computational neuroscience for further prevention of nervous diseases.

Swarmalators, entities that combine the properties of swarming particles with synchronized oscillations, represent a novel and growing area of research in the study of collective behavior. This review provides a comprehensive overview of the current state of swarmalator research, focusing on the interplay between spatial organization and temporal synchronization. After a brief introduction to synchronization and swarming as separate phenomena, we discuss the various mathematical models that have been developed to describe swarmalator systems, highlighting the key parameters that govern their dynamics. The review also discusses the emergence of complex patterns, such as clustering, phase waves, and synchronized states, and how these patterns are influenced by factors such as interaction range, coupling strength, and frequency distribution. Recently, some minimal models were proposed that are solvable and mimic real-world phenomena. The effect of predators in the swarmalator dynamics is also discussed. Finally, we explore potential applications in fields ranging from robotics to biological systems, where understanding the dual nature of swarming and synchronization could lead to innovative solutions. By synthesizing recent advances and identifying open challenges, this review aims to provide a foundation for future research in this interdisciplinary field.

Collective dynamics in multi-agent systems provide a powerful framework for understanding how coherent group-level patterns can emerge from simple interactions between individuals. Such phenomena are observed in many natural and artificial systems, including animal groups, robotic swarms, and distributed decision-making processes. In many situations, agents are not only characterized by their spatial motion, but also by internal states, e.g., opinions or preferences, which evolve through interactions with peers. Understanding how these internal states influence collective motion, and how spatial organization in turn affects internal dynamics, remains an important challenge. In this work, we propose a model of coupled collective motion and opinion dynamics. The spatial dynamics are governed by attraction–repulsion interactions, while the internal dynamics are described by a Deffuant-type opinion model. Our results show that the confidence threshold of the opinion dynamics plays a key role in controlling the number of opinion clusters, whereas the strength of the opinion-dependent spatial attraction determines whether these clusters spatially merge or remain separated. In addition, for the full-consensus state, we derive the expression for the radius of the stationary swarm distribution when a nonlinear attraction kernel is used, using a semi-analytical approach. The proposed framework may be useful for studying collective decision-making, animal group behavior, and coordination strategies in swarm robotics.

Dengue transmission is strongly influenced by climatic variability, and understanding how weather affects mosquito ecology is essential for both interpreting outbreaks and improving surveillance. In this study, we analyze weekly dengue incidence together with temperature, rainfall, and humidity data from Brasilia, which serve as the basis for deriving empirical, climate sensitive entomological parameters describing mosquito development, mortality, and aquatic stage dynamics. Using these weather informed parameters, we formulate and calibrate a six-compartment dengue transmission model that incorporates the mosquito aquatic stage. The model is employed to investigate the underlying transmission mechanisms, including parameter sensitivity, the temporal evolution of the basic reproduction number R0(t) and the influence of climatic drivers on system behavior. The epidemiological relevance of R0(t) is examined through comparison with weekly reported dengue incidence. Additional analyses such as bifurcation assessment and evaluation of vector-control and treatment-related parameters provide further insight into how environmental conditions and interventions shape transmission potential. Complementing the mechanistic analysis, we conduct a data-driven forecasting study using several statistical and machine learning approaches (Neural Networks, Support Vector Regression, Extreme Gradient Boosting, Seasonal ARIMA, and Long Short Term Memory networks) applied to the epidemiological and climate datasets. This component examines the predictive performance of diverse methods across linear and nonlinear temporal patterns, highlighting the role of climate information in improving incidence forecasts. By integrating climate derived entomological characterization, mechanistic modeling, and data driven forecasting within a unified framework, this study enhances our understanding of climate-dengue interactions while also evaluating practical approaches for short term outbreak prediction.

Synchronization is conventionally understood as the emergence of a phase-locked collective state among interacting dynamical units. However, extending this notion to systems whose dynamical variables are defined on higher-dimensional simplices introduces fundamentally new constraints arising from the topology of the underlying simplicial complex. In the simplicial Kuramoto model, nontrivial topological cycles give rise to a higher dimensional harmonic subspace that is unaffected by the coupling and can therefore drift indefinitely, preventing a globally synchronized state. To resolve this we employ Hodge decomposition on simplicial Kuramoto dynamics and investigated the components. Despite this topological obstruction, we show that the simplicial Kuramoto model admits fixed-point states in the exact and coexact sectors of the Hodge decomposition above critical coupling strengths, which we derive analytically for both sectors. This decomposition provides a generalized notion of synchronization in which the non-harmonic components converge to fixed states. We further investigate the robustness of these fixed-point states to external perturbations. Excluding the drifting and non-interacting harmonic component, the perturbation response is governed by the spectrum of weighted Laplacian and recovers a Kirchhoff index dependence analogous to standard Kuramoto case. In contrast, the harmonic sector is non-dissipative, and consequently the fragility of the system increases with the dimension of this topological subspace. We characterize this effect numerically using triangulated tori with varying first Betti number and find a superlinear scaling relation between system fragility and the dimension of the harmonic sector.

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely, (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons, and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in the response network connected to the drive increases, the onset of control occurs earlier, indicating a scaling advantage of the method.

The monkeypox epidemic poses a serious global health threat, making effective control strategies essential. Using a mechanistic SEIR (Susceptible-Exposed-Infectious-Recovered) model, this study incorporates both pro-and anti-vaccination attitudes among susceptibles to examine their impact on transmission. Sensitivity analysis via partial rank correlation coefficients (PRCC) identifies key parameters affecting the basic reproduction number (R0). The model reveals both forward and backward bifurcations, indicating potential for stable infection states and persistent epidemics. To address vaccination behavior, a coupled vaccination game based on imitation dynamics is introduced. Results show that higher imitation rates increase pro-vaccine adoption and reduce infections. The study highlights the role of social dilemmas, where low pro-vaccine uptake and frequent strategy switching worsen outbreaks. High vaccination costs further reduce social payoff, but strong social learning still promotes uptake, even with low susceptibility or high costs. Overall, social learning strategies can enhance vaccination rates and curb monkeypox spread.

Understanding how cooperation persists despite the advantage of selfish behavior remains a central challenge in evolutionary dynamics. Classical models of public goods dilemmas predict dominance of defectors, yet natural and social systems often sustain cooperation. We study an eco-evolutionary public goods game on complex networks where cooperators and defectors diffuse at different rates. When the isolated system is in a defector-dominated coexistence regime, faster dispersal of defectors than cooperators leads to a symmetry-breaking transition that produces localized clusters of cooperators. In heterogeneous networks, nodes with higher connectivity become significantly more likely to exhibit cooperative dominance. A degree-based mean-field reduction supports this result by showing that network connectivity controls an effective coupling strength proportional to node degree, thereby producing a bifurcation that separates defector-dominated and cooperative states. We also address why not all hubs become cooperative by means of a multistability analysis. These results reveal how asymmetric mobility and heterogeneous connectivity jointly promote cooperation in structured populations.

The Murali-Lakshmanan-Chua (MLC) circuit is a well-recognized prominent nonlinear, nonautonomous, and dissipative electronic circuit having a versatile chaotic nature. Unraveling the dynamical synergy responsible for the genesis of extreme events in nonlinear dynamical systems is a prolific and spellbinding research area. The present study unveils the dynamical exposition of emerging extreme events in the MLC circuit concerning two different events being defined in the system. The large expansion of the chaotic attractor following the PM intermittency route plays the crucial role as the precursor behind the emergence of extreme events in the system. Our main finding reveals the prevalence of a force field due to the presence of externally applied periodic force in the system that creates the dynamical synergy that compels the chaotic trajectory traversing in its phase space to be largely deviated from the residing space, and this large deviation shows the signature of extreme events. Apart from the force field explication, we explored another two dynamical aspects that also interpret the mechanism behind the genesis of extreme events as the large deflection of the chaotic trajectory in the system: the decomposition of the phase space in stable and unstable manifolds concerning slow-fast dynamics and using Floquet multipliers. These two different aspects of calculations of the stable and unstable manifolds explicate the large excursion of the chaotic trajectory as extreme events from two different perspectives. We also analyzed the rare occurrences of the extreme events statistically using extreme value theory: the threshold excess values follow the generalized Pareto distribution, and the inter-extreme-spike-intervals follow the generalized extreme value distribution.

We study a variant of the one-dimensional swarmalator model where the phase dynamics are pulsatile, governed by a phase-response curve and a pulse function, similar to the Winfree model of regular oscillators. Previously, we studied the idealized case where the individual swarmalators were identical; we generalize this to the more realistic case of non-identical swarmalators, where the natural frequencies are randomly distributed. We find that this heterogeneity leads to new kinds of collective dynamics. These states may be observable in groups of Japanese Tree frogs, circularly confined sperm, or other types of real-world swarmalators.

We study search processes in a complex environment using the strategy of stochastic resetting. A common occurrence in these environments is targets with finite reactivity. Stochastic resetting has emerged as a powerful mechanism for optimizing search processes by curtailing long, unproductive excursions inherent to diffusive dynamics. Most theoretical studies, however, assume perfectly absorbing targets – an idealization that overlooks the finite reactivity commonly encountered in realistic chemical and biological systems. In this work, we investigate the interplay between stochastic resetting and finite-target reactivity in reaction - diffusion processes. Considering a one-dimensional system with multiple reactive targets, we demonstrated that the target reactivity modifies the optimization landscape. We uncover distinct regimes in which resetting enhances transport efficiency towards specific targets based on their chemical kinetics. As a consequence, the optimal resetting rate becomes intrinsically reactivity dependent. Our results identify target reactivity as a crucial control parameter governing stochastic transport and provide insights into reaction-diffusion processes in complex media.

Ebola virus disease is a potential threat to global health, which spreads rapidly in a short period of time to different parts of the world, especially in Africa. It typically originates from human contact with domestic or wild animals and spreads through direct and indirect human contact, making containment highly challenging. Here, we formulate a novel seven-compartmental SVIHRQG fractional-order epidemiological model involving susceptible, vaccinated, infected, hospitalized, recovered, and deceased (due to Ebola) populations, as well as environmental pathogens. We study the dynamics and control strategies of this model incorporating memory effects using the Caputo fractional-order derivative. A normalized forward sensitivity analysis of the basic reproduction number is employed to identify the parameters exerting the highest influence on the model. Changes in the reproduction number trigger a stability switch between the disease-free and endemic equilibrium points through a transcritical bifurcation. The model is calibrated using the nonlinear least-squares method on data from the Ebola outbreak in North Kivu, Democratic Republic of the Congo (2018–2020), with nonparametric bootstrap uncertainty analysis. A comparative analysis using data-fitting performance metrics indicates that the memory-inclusive fractional model better captures the reliability, robustness, and accuracy of real data trends than the classical integer-order model. In addition, an optimal control framework incorporating vaccination and treatment strategies is developed to identify effective intervention policies. Cost-effectiveness analysis indicates that the combined control strategy significantly reduces infection levels at a lower cost relative to scenarios without intervention.

Data-driven predator-prey modeling remains a challenging problem in ecological dynamics. In this study, we develop a prey-predator model to examine the interactions between elk and wolves in Banff National Park, explicitly incorporating prey refuge, inter-regional movement, and predation pressure. The system consists of two prey populations-Banff townsite elk and Bow Valley elk and wolves as the predator population. Through linear stability analysis, we derive the critical threshold of the Bow Valley elk production rate (/i) and determine both the existence and direction of Hopf bifurcations. Furthermore, global stability of the equilibrium point is established using a Lyapunov function approach. The model is parameterized with empirical population data to ensure biological realism. Through sensitivity analysis, we found /i as the most influential parameter affecting the populations. Our analysis reveals that increasing /i leads to the extinction of the Banff elk population after transient oscillations, while the Bow Valley elk and wolf populations undergo a transition from stable equilibria to sustained limit cycle oscillations. These findings highlight the role of prey refuge in shaping elk-wolf coexistence and provide new insights into population persistence under ecological constraints.

The elk - wolf model with movements between refuge and open habitat was put forward in Maji et al. (Appl. Math. Comput. 514 (2026)), which is rigorously re-examined in this remark. We re-evaluate the local and global stability analyses, especially the construction of the Lyapunov function, and provide mathematical clarifications on boundedness, model formulation, and the existence of equilibria. The sensitivity and numerical results are re-examined for consistency and re-producibility, and the Hopf bifurcation conditions are rederived using the proper transversality criteria. The purpose of this note is to support future studies of predator-prey systems based on refuges by offering mathematically consistent conditions.

Dispersal networks critically shape the fate of ecological communities, yet the mechanisms linking connectivity and persistence remain poorly understood. We show that an interplay between asymmetric dispersal and asynchronous dynamics across patches in a dispersal network can prevent predator extinction across broad dispersal ranges, even in identical environments in which synchrony usually drives ecosystems to collapse. Unlike classical rescue effects based on environmental heterogeneity or equilibrium states, this mechanism emerges from non-equilibrium dynamics, specifically from transient chaotic dynamics. Dispersal coupling perturbs local trajectories in patches facing extinction and reinforce chaotic motion, thereby sustaining chaotic oscillations indefinitely. Strikingly, only minimal connectivity is required: small-world networks with a few long-range links suffice to rescue predator populations. These findings reveal a counterintuitive principle that limited, well-placed connectivity can harness chaos to maintain biodiversity in fragmented landscapes.

Dengue fever is a mosquito-borne viral disease that continues to pose a substantial public health burden in tropical and subtropical regions. Although most existing studies are based on deterministic formulations, environmental variability and behavioral responses can significantly influence transmission dynamics. In this work, we formulate and analyze a stochastic dengue transmission model that incorporates media-driven awareness, nonlinear treatment responses, and environmental noise. The stochastic system is shown to be well posed by establishing the existence, uniqueness, and positivity of global solutions. The model parameters are estimated by calibrating the deterministic counterpart of the stochastic system against the reported data on dengue incidence, demonstrating good agreement between simulations and observations. The basic reproduction number is derived and sensitivity of the parameters is assessed using partial rank correlation coefficients under uncertainty to identify key drivers of transmission. Analytical conditions for noise-induced disease extinction are obtained, revealing that sufficiently strong environmental fluctuations can suppress endemic persistence. The impact of varying noise intensities on long-term dynamics is further characterized. Finally, we develop a stochastic optimal control framework that integrates awareness-based prevention and treatment interventions, providing a theoretical basis for evaluating control strategies under environmental uncertainty.