The network dismantling(ND)problem,which involves identifying the minimum set of nodes that will cause a system to collapse if re-moved,remains a critical challenge in network science.

In this paper, we consider the bifurcations and exact solutions in the symmetric a phi(4n)-b phi(2n)|phi|-phi(2) triple-well model. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to some level curves, we derive possible exact explicit parametric representations of the smooth periodic solution, homoclinic solutions, as well as heteroclinic solutions.

Chaos control involves applying small perturbations to chaotic systems to achieve desired behaviors. Pinning control, a feedback control strategy designed for complex networks, is widely used for managing large-scale coupled dynamical systems. While much of the research on pinning control has focused on stabilizing chaotic networks at their equilibria, this approach is less applicable to biological systems, where equilibrium often corresponds to cell death. Instead, controlling chaotic networks to reproduce realistic biological behaviors could provide valuable insights into mitigating pathological disorders. Atrial fibrillation (AF) is a rapid, irregular heart rhythm caused by chaotic electrical impulses. AF can result in blood clots, increasing the risk of heart failure, stroke, and other serious complications. In this study, we investigate a heart network model based on the standardized segmentation of atria and ventricles, described by the American Heart Association. Using the pinning control method, we demonstrate the transition of a chaotic cardiac rhythm in AF mode into a normal periodic rhythm, offering a potential strategy for treating AF-related conditions.

This article addresses specified-time distributed Nash equilibrium seeking (ST-DNES) problems for aggregative games over unbalanced directed communication networks. Each player's cost function is influenced by both its own strategy and an aggregate of all other players' strategies. First, a new research framework is developed, named specified-time collaborative planning and seeking. Under this framework, a class of ST-DNES algorithms is designed with a specified-time distributed average estimator (ST-DAE) over undirected networks based on Pontryagin's maximum principle. Then, to deal with the asymmetry of unbalanced directed networks, a couple of improved ST-DNES algorithms are developed with two different types of ST-DAEs, called integral-surplus and balance-compensator based ST-DNES algorithms, respectively. With the help of these two ST-DAEs, the ST-DNES problem over unbalanced directed networks is successfully solved. It is noticed that, the balance compensator based ST-DNES algorithm needs to sort all players with different numbers if allowed. The integral-surplus based ST DNES algorithm does not require sorting but needs out-degree information of players in the network. One may select different algorithms in different situations. Finally, the proposed ST DNES algorithms are used to solve an energy consumption game problem, which proves their effectiveness. It is highlighted that this is the first time to establish the specified-time convergence of aggregative games over unbalanced directed communication networks.

This work presents a novel compact analog circuit unit for implementing piecewise-linear functions. With an integrated ICs-based modular expandable architecture, the circuit unit allows flexible configuration of breakpoints in the piecewise-linear function with external voltages, thereby achieving high precision and scalability. Since dynamics editing can be conveniently applied to reconstruct attractors, this unit is particularly useful for constructing multi-wing attractors. Using the editing function, multi-dimensional multi-wing attractors of the diffusionless Lorenz system are reconstructed and realized. Experiments demonstrate the efficiency of cell attractor selection and multi-wing organization. By adjusting the threshold voltages of the module, any number of multi-wing attractors in different dimensions can be obtained. This circuit unit can be readily applied to the construction of multi-wing/multi-scroll attractors, offering a valuable analog circuit schematic for chaotic signal generation and chaos-based secure communication.

This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying systems, upon which a robust controller is designed to ensure that the resulting closed-loop system is input-to-state stable with respect to the Koopman approximation error. The error of the lifted system model learned through the Koopman-based method increases over time due to the time-varying nature of the nonlinear time-varying system. To address this issue, an online iterative update scheme is incorporated into the learning process to update the lifted system model, aligning it more precisely with the nonlinear time-varying system by integrating the updated data and discarding the outdated data. A necessary condition for the feasibility of the proposed iterative learning method is derived. In order to reduce unnecessary system updates while ensuring the prediction accuracy of the lifted system, the update mechanism is enhanced to determine whether to update the lifted system and meanwhile to reduce updates that deteriorate the fitting performance. Numerical simulations on the Duffing oscillator, the serial manipulator, and the synthetic biological network system are presented to demonstrate the effectiveness of the proposed method for the prediction and control of unknown nonlinear time-varying systems. The results show that the proposed approach outperforms existing methods in terms of approximation accuracy and tracking accuracy. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This work is concerned with mean-square bipartite containment of second-order multileader multiagent systems (MASs), contaminating compound noise, and antagonistic information under a fixed or Markovian switching signed topology. A new class of bipartite containment control protocols based on absolute velocity and relative position information is designed using signed graphs, and a time-varying control gain is introduced to eliminate the combined effect of additive and multiplicative noises. For the case under fixed topology, sufficient conditions for achieving bipartite containment are derived by using the Lyapunov function method. Then, it is extended to the case of nonlinear dynamics. Specific convergence values for all leaders and followers are obtained. For the case under Markovian switching topology, the boundedness of the agents’ states and noise intensity is proved by employing the extended second-moment method. By utilizing properties of stochastic matrices and the ergodicity of Markov chains, the second moments of the bipartite containment errors are estimated to obtain mean-square bipartite containment conditions. In addition, the corresponding convergence rates of mean-square errors are explicitly expressed. The effectiveness of the theoretical results is finally verified through numerical simulations.

In this paper, the emergence of Parrondo’s paradox for fractional-order (FO) dynamical systems driven by the Parameter Switching (PS) algorithm is investigated. The PS algorithm runs by switching the control parameter within a predetermined set of values during the numerical integration of the initial value problem, so that the resulting trajectory approximates the existing attractor corresponding to the averaged parameter. By extending the operation and application of PS algorithm to FO systems, it is demonstrated analytically, numerically, and experimentally verified that Parrondo’s paradox occurs in FO systems. The analysis relies on the convergence properties of the PS algorithm applied via the fractional Adams-Bashforth-Moulton (ABM) scheme, showing that the switched solution approximates the averaged solution accurately. Numerical simulations on a dark-matter–dark-energy system, on a highly nonlinear system, and also on an electronic circuit implementation of a FO Chen system all confirm the presence of Parrondo-like behavior. The findings quantify the convergence of the PS algorithm in FO systems and confirm that the switching scheme consistently yields the paradoxical behavior predicted by the averaged parameter model.

Multilayer complex dynamical networks have large numbers of nodes, complex topological connections, and various hierarchical structures. Each network layer therein has unique functions and characteristics, working together through interlayer coupling effects. The complete topological structure of such a multilayer network is usually difficult to fully determine. Can we employ the topological information of one known layer to identify the unknown intralayer topology of another layer in the multilayer network? In this article, a novel topology identification method is proposed for revealing the unknown intralayer topology of one layer using information of another known layer. The interlayer coupling effect regulation term and the topological difference term are first introduced into the design of a topology observer. Based on the generalized synchronization principle, an adaptive topology observer is developed to identify the complex topology and monitor sudden topology changes of the other network layer. The proposed scheme allows to freely select a target layer and a known layer from the given multilayer complex dynamical network. Numerical simulations verify the effectiveness of the proposed intralayer topology identification method.

This paper analyzes synchronization performances and formulates synchronizability criteria for multi-weighted complex dynamical networks under pinning control. General synchronization conditions and a pinning controller design method are derived. On this basis, synchronizability criteria are established by analyzing the effects of network topology and coupling strength on pinning synchronization. Furthermore, a synchronizability criterion is derived based on the eigenvalues at the unpinned nodes, which takes into account multiple attributes and effectively reduces the global computational complexity as the number of pinned nodes is varied or the pinning strategy is adjusted. Finally, under the proposed synchronizability criteria, this paper systematically analyzes the impact of key parameters on the synchronizability of multi-weighted BA and NW networks. Experimental results demonstrate that pinning high-degree nodes is more effective when the number of pinned nodes is small, whereas pinning low-degree nodes becomes more advantageous as the number of pinned nodes increases, for both multi-weighted BA and NW networks. For multi-weighted NW networks, the edge-addition probability not only affects the network synchronizability but also plays a key role in determining the critical number of nodes for pinning strategies. This study reveals the significant influence of multiple weight attributes, total in-degree of nodes, and coupling structures on the synchronizability of multi-weighted networks under pinning control, offering valuable insights in optimizing pinning strategies for improving the network synchronizability.

Neuromorphic circuits that simulate the sleep cycle serve as a critical bridge between neuroscience and hardware implementation. To address the limitations of conventional circuits, which are often complex and lack mechanisms for biological plasticity and memory, this paper presents two highly compact memristor-transistor hybrid neural network circuits designed to simulate transitions between different sleep stages. The core innovations of this design are: 1) utilizing the non-volatile memory property of individual memristors to directly implement the retention of neuronal activation states in hardware, thereby simulating the persistence of sleep stages; and 2) employing a specific memristor connection topology to accurately simulate the indirect and direct inhibitory functions of gamma-aminobutyric acid (GABA)-ergic neurons in the rostromedial tegmental nucleus (RMTg) region on neurons in the laterodorsal tegmentum (LDT) and laterodorsal hypothalamus (LH) regions, using a minimal number of components. Based on this design, corresponding circuits are constructed and simulated using PSPICE. The results demonstrate that this memristive neural network can successfully simulate state transitions between wakefulness, non-rapid eye movement (NREM) sleep, and rapid eye movement (REM) sleep by modelling the activation of GABAergic neurons in the RMTg and their subsequent inhibitory effects in the LDT and LH regions. The designed circuits exhibit a high degree of functional alignment with the target biological neural networks. Furthermore, simulation analysis confirms that the circuit can not only represent normal sleep architecture but also, by adjusting the initial states of key memristors, quantitatively replicate and differentiate the sleep structure fragments between healthy elderly individuals and young adults.

This paper studies the distributed secure state estimation problem in cyber-physical systems under sparse sensor attacks, by employing an adaptive dynamic gain modulation strategy. Unlike most existing attack detection and isolation-based strategies, a dual-layer collaborative state estimation framework based on attack suppression is established. The framework integrates decentralized and distributed observers, thereby decoupling attack suppression from residual feedback. By analyzing the dynamic behaviors of state deviations between the two observer layers, a universal dynamic suppression gain is derived to guarantee the robustness against sparse attacks. Furthermore, a distributed adaptive dynamic gain modulation strategy is introduced to avoid centralized processing, which enhances the applicability of the attack suppression mechanism while preserving the estimation accuracy. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed framework.

This article studies the problem of resilient distributed state estimation for sensor networks subject to location-varying Byzantine cyberattacks, focusing on the cooperative estimation of a static vector. The existing mean-subsequence-reduced-based algorithms rely on dimension-wise ordering to resist Byzantine attacks, leading to poor scalability in high-dimensional systems. To overcome this issue, the signum operator and absolute value function are employed to decouple the high-dimensional attack characteristics, based on which a norm-based max-discard mechanism (NMDM) is proposed to isolate location-varying Byzantine attacks. Building upon this foundation, a resilient distributed state estimation algorithm integrated with NMDM is developed to achieve consensus estimation of high-dimensional vectors, irrelevant to the switching frequency of attack locations. Finally, two numerical simulation examples are presented to demonstrate the effectiveness and advantages of the proposed algorithm.

Incentive-based control mechanisms in game-theoretic models aim to steer players toward socially desirable strategies through appropriately designed utility rewards or penalties. In this paper, we propose an algebraic framework for incentive-based control in networked evolutionary coordination games (NECGs) under asynchronous myopic best-response dynamics. We establish a fundamental connection between the reward policy and the attainability of a desired equilibrium, demonstrating that a fully cooperative equilibrium is implementable if and only if there exists a reward vector that makes it reachable from the initial fully non-cooperative strategies in the incentivized NECG. Moreover, leveraging the strategy profile reachability sets, we demonstrate that the incentive control problem reduces to verifying the reachability of the set associated with the desired equilibrium. We prove that the reachable set of the desired equilibrium in the original NECG is contained within that of its incentivized counterpart. This, to some extent, simplifies the verification for computing the reachable set of the desired equilibrium in the incentivized NECG. Finally, we show an example to illustrate the proposed result.

Different types of attractors of a dynamical system can be collected into the same phase space to form coexisting attractors, from which various patterns of multi-wing attractor can be created. Homomorphic and heteromorphic multi-wing attractors can be customized by aggregating different types of system solutions through a piecewise linear function combined with the regulation of the distances between these attractors. This work proposes a novel construction method for multi-wing chaotic attractors by dynamics editing, by which one-dimensional and two-dimensional homomorphic and heteromorphic multi-wing attractors are realized through the selection of coexisting attractors and their mutual distances. Due to the excellent pseudo-randomness of chaotic sequences, multi-wing chaotic attractor is found with great value in the field of Internet of Things (IoT) information encryption. After the generation of multi-wing chaotic attractors based on the CH32V307 microcontroller, a new type of chaotic encryption scheme is constructed for image encryption, demonstrating the excellent performance of the pseudo-randomness from the newly derived multi-wing chaos.

Higher-order networks provide a powerful framework for modeling complex interaction dynamics that go beyond simple pairwise relationships. However, on the other hand, in many real-world scenarios, the underlying network topology is not directly observable, but only time-series data of node dynamics are available. The structure of higher-order networks is inherently more intricate than that of traditional pairwise networks. These make the accurate reconstruction of higher-order networks a critical challenge. Existing methods are typically limited by insufficient accuracy, and they overlook the inherent symmetry priors in undirected higher-order networks. To address this issue, we incorporate symmetry priors into the reconstruction process by embedding symmetric constraints into the iterative equation and the solving procedure by employing the block coordinate descent method. The proposed approach ensures reconstruction accuracy while reducing computational complexity. Theoretical analysis and numerical experiments show that our method achieves accuracy comparable to the conventional global method with efficiency close to the point-by-point method, providing a practical and scalable methodology for higher-order network reconstruction.

This paper presents a novel lightweight privacy-preserving control protocol for leader-following consensus in discrete-time multi-agent systems, tailored for consumer IoT applications such as electric vehicles (EVs) and autonomous aerial vehicles (AAVs). By employing general decaying signals to mask sensitive user data, including the initial states of agents (e.g. starting positions or velocities), the protocol enables devices to track a leader's trajectory, e.g., navigation paths for AAV swarms or energy-efficient velocity profiles for vehicular platooning, while safeguarding privacy. We reformulate the problem as the stability of a discrete-time system with diminishing disturbances and derive sufficient tracking conditions using a new convergence lemma for infinite sequences. Control gains are computed efficiently via a modified algebraic Riccati equation. Unlike conventional methods reliant on computationally intensive encryption or restrictive exponential decay, our approach leverages flexible, locally selectable decaying functions, enhancing privacy and adaptability while maintaining a lightweight design. Numerical simulations of AAV formation and vehicular platooning demonstrate rapid convergence to the leader's trajectory with lightweight privacy protection robust against curious agents and eavesdroppers, showcasing the protocol's superior balance of control accuracy, data security, and computational efficiency, desirable for consumer electronics.

Locally active memristor (LAM), which has an ability to amplify fluctuations, is a natural component for constructing artificial neuron circuits. This article proposes a novel third-order neuron circuit by paralleling two LAMs and a capacitor. First, two parallel LAMs are equivalently modeled as a second-order LAM to facilitate theoretical analysis. Regarding the third-order neuron, the parameter design and operating condition are obtained by calculating its small signal impedance function's poles or Jacobin matrix's eigenvalues. It is demonstrated that the neuron exhibits various neuromorphic behaviors, including periodic spiking, chaos and burst-number adaptation. Due to the two different LAMs, the proposed third-order system has multiple equilibrium points, leading to the generation of coexisting attractors. Interestingly, the generated chaotic attractor does not revolve around a single unstable equilibrium point, but is located between two unstable equilibrium points. Furthermore, the emergence of oscillating behaviors is dependent on the distance between the two unstable equilibrium points. Detailed theoretical and simulation analysis are presented to investigate the neuron dynamics and provide an explanation for the observed neuromorphic behaviors. Finally, physical circuit implementation of the neuron is constructed based on the memristor emulator, which also demonstrates the practicability of the proposed neuron model and the correctness of the theoretical analysis.