This paper proposes a symmetric quantum Stackelberg duopoly model based on the Frankiewicz quantum method with linear demand and cost functions. The Frankiewicz quantum technique has seldom been applied in the Stackelberg duopoly, and, to the best of the authors' knowledge, this is the first study to use a linear cost function in this context. The game focuses on two players with different expectations. The leader is bounded rational, whereas the follower is adaptable. The equilibrium points of the game model are computed using the backward induction approach, and their stability is numerically examined in terms of various factors. It has two equilibrium points: the subgame perfect equilibrium point and the quantum boundary equilibrium point, which has no economic significance. This model shows chaotic behavior, as evidenced by time series analysis (sensitivity to initial conditions) and phase plots. Furthermore, the complex dynamics of the model, as impacted by various model parameters, are thoroughly examined using one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, and Kaplan-Yorke dimension charts. This research can aid in analyzing and comprehending unexpected actions and strategic circumstances in this game. Understanding the factors that cause chaotic behaviors allows participants (financial firms) to optimize their strategy when confronted with such scenarios.

For the existence of the external perturbation on the atmospheric system, the idealized Lorenz system cannot be used to describe the local characteristics of the atmospheric system accurately. From the opinion of mathematical physics, the failure of the description for local characteristics of the perturbed atmospheric system by the idealized Lorenz system is resulted from the symmetry-breaking effects on the local structure the solutions for the system, including the Lorenz attractor. This study aims to precisely quantify the symmetry-breaking degree of the rotation invariant law for the attractors in a perturbed Lorenz system to permit the reproduction on its local characteristics accurately. The attractors of the perturbed Lorenz system are reproduced employing the second-level fourth-order symplectic Runge-Kutta scheme firstly. The structure-preserving properties of the scheme are illustrated by the tiny relative energy error in the conservative field of the Lorenz system, which verifies the validity of the simulation results indirectly. The symmetry-breaking degree for the rotation invariant law of the attractors in the system is characterized by the quantized error defined as the Euclidean distance between the points on the trajectories of the rotated part and of the unrotated part at the same moment. The symmetry-breaking phenomenon characterized by the quantized error goes through three stages in sequence, including the slow growth stage, the quick growth stage, and the oscillation stage. In addition, a pair of Lorenz attractors with the approximate rotation invariant property are observed when the quantized error is in the slow growth stage or in the quick growth stage. From the numerical results, it can be found that, the perturbation may cause the periodic step increase (the amplitudes of steps are doubling increase approximately) of the error with the time elapse even if the perturbation is tiny, which leads to more serious damage to the stability of the system. The main contribution of this work is providing an approach to predict the local stability of the Lorenz system, which may benefit for the accuracy of meteorological forecast or the simulation of specific atmospheric phenomena.

In practical engineering applications, curved structures rarely conform to idealized rectangular or circular planforms and often involve far more intricate geometries. Among these, L-shaped spherical panels have emerged as a structurally significant form, found in subsystem interfaces, aerospace fuselage junctions, complex biomedical shells, and multifunctional architectural surfaces. This study explores the free damped-vibration behavior of such panels constructed from a graphene platelet (GPL)-reinforced magnetorheological elastomer (MRE) nanocomposite. Unlike conventional elastic matrices, the MRE base material exhibits time- and fielddependent viscoelastic behavior, influenced by both magnetic field intensity and ferromagnetic content. This behavior is mathematically formulated through an experimentally validated generalized Kelvin-Voigt-type model, tailored to represent the storage and dissipation characteristics of the matrix under dynamic excitation. The reinforcing particles are graded through the panel thickness. The effective elastic properties of the composite are homogenized using the Halpin-Tsai micromechanical model, accounting for the influence of GPL content and sizes. To address the geometric complexity, a hybrid element-based GDQ (generalized differential quadrature) approach is developed. The L-shaped spherical panel is subdivided into rectangular elements, each governed by equations derived using Hamilton's principle, first-order shear deformation theory, and Sander's straindisplacement relations. Discretization via quadrature nodes enables the GDQ method to transform the governing PDEs into an efficient algebraic system. The global system is constructed by enforcing both displacement and force continuity at shared nodes and applying appropriate boundary conditions. The proposed framework achieves excellent accuracy in capturing frequencies and loss factors, demonstrating its capability for efficient dynamic analysis of non-standard. In addition to validating the accuracy of the proposed approach against benchmark problems, the study reveals distinct mode-switching and mode-jumping phenomena triggered by changes in geometric parameters-highlighting the sensitivity of vibrational behavior to panel shape and reinforcing the need for precise modeling in advanced smart structures.

This study establishes a nonlinear dynamic model for an electric vehicle motor-reducerdifferential electromechanical coupling system to investigate its vibration response characteristics under operational conditions. The model integrates key excitation sources including motor unbalanced magnetic pull, time-varying bearing forces from both tapered roller and deep-groove ball bearings, helical and bevel gear mesh excitations, and tooth surface friction effects. Dynamic responses are analyzed under rotational speed excitation with appropriate damping considerations: rotor support damping for the motor-bearing subsystem and mesh damping for the gear transmission subsystem. Model validation is performed through systematic comparison between simulation results and experimental bench data. The analysis reveals that the peak vibration amplitude of the coupled system occurs within the medium-to-low speed range, with the differential mechanism exhibiting a significantly broader instability region compared to the motor and reducer components. These findings provide critical insights into vibration mechanisms and stability thresholds in electric vehicle powertrain systems.

UAV object detection remains challenging due to large scale variation, dense small objects, frequent occlusion, and complex background interference. Existing CNN-based detectors are often limited by weak small-object representation, while Transformer-based detectors may not adequately preserve local details in dense aerial scenes. This paper proposes a dual-path detection framework that integrates frequency-domain enhancement with large-kernel convolution and Transformer-based global modeling. An FFT Large-Kernel Convolution (FFLKC) module is introduced to enhance high-frequency details and enlarge the effective receptive field. A Transformer pathway with Full-Process Feature Attention (FPFA) is designed to strengthen long-range dependency modeling and semantic representation. A Frequency-Semantic Memory-guided Adaptive Fusion (FMSAF) module is further employed to integrate local detail features and global contextual information. Experiments on UAVDT and VisDrone demonstrate that the proposed method achieves superior overall detection performance and stronger small-object perception than mainstream detectors. The method reaches 58.7 AP and 51.8 APS on UAVDT, and 39.4 AP and 30.5 APS on VisDrone. Qualitative and quantitative results verify the effectiveness of the proposed design in improving detection quality under complex UAV backgrounds.

Explosive synchronization (ES) describes an abrupt and hysteretic transition from incoherence to collective order and has been widely studied in static networks. Here, we show that temporal variability of network connectivity can fundamentally reshape this transition. We investigate inertial Kuramoto oscillators evolving on stochastically rewired random networks, where links are continuously replaced at controlled rates, allowing us to tune the interplay between inertia and topological dynamics. Our results reveal that temporal rewiring can both induce and suppress ES depending on the network density and the switching timescale. Sparse networks display ES only under very slow or very rapid switching, whereas denser networks exhibit robust explosive transitions across a broad parameter range. Increasing the rewiring probability generally promotes abrupt synchronization, but excessively frequent rewiring weakens hysteresis and reduces bistability. A systematic exploration across different degrees confirms that ES is most prominent when moderate-to-high rewiring probability is combined with rapid switching, whereas small rewiring probability favors continuous transitions. These findings demonstrate that temporal randomness is not merely a perturbation but a key control mechanism for abrupt collective behavior, representing how time-varying connectivity governs the onset, robustness, and disappearance of ES in dynamical networks.

In this study, the nonlinear dynamic model of the gear transmission system of the wind energy harvesting triboelectric nanogenerator and the relative motion model between the friction material layers are established to explore the dynamic characteristics and power output characteristics of the system under different input parameters. Firstly, considering various factors, a nonlinear dynamic model of the friction nanogenerator gear transmission system is established. Secondly, the potential energy method is used to calculate the time-varying meshing and stiffness of the gear. Then, the solution of system dynamic equation is used to draw time domain diagram, spectrum diagram, Poincare section diagram and displacement bifurcation diagram, and compared with the experimental results to verify. Finally, the relative sliding model between the electrodes of the triboelectric nanogenerator is established, and the electrode parameters are substituted. The relationship between the open-circuit voltage and shortcircuit current and the system parameters is explored by drawing two-dimensional and threedimensional open-circuit voltage and short-circuit current images. The results show that with the increase of meshing stiffness and external excitation frequency, the open-circuit voltage and the short-circuit current will increase, however, the efficiency of power generation will decrease accordingly; Through comparative experiments, the accuracy of the model is verified. To improve the power generation and power generation efficiency as much as possible under the condition of maintaining stable operation of the system, the external excitation frequency and the meshing stiffness should be selected in the appropriate range.

This paper introduces a novel memristive FitzHugh–Rinzel neural oscillator and investigates its chaotic dynamics using bifurcation diagrams and Lyapunov exponents. A neural network based on this oscillator is constructed to study synchronization control under a non-local coupling structure, considering electrical, chemical, and electrochemical coupling. The results show that synchronization occurs at weaker coupling strengths under chemical coupling than electrical coupling, with a non-monotonic decrease in synchronization error as the coupling strength increases. However, at high chemical and electrochemical coupling strengths, the system undergoes oscillation death, where neurons cease oscillating and reach a stable state. These findings highlight the distinct roles of chemical and electrochemical interactions in shaping neural network synchronization and collective dynamics.

This study investigates synchronization dynamics in a three-layer network of memristive Hindmarsh-Rose (m-HR) neurons with a central hub node. The outer layers consist of globally coupled identical m-HR neurons, while the middle layer contains a single hub neuron that relays signals between the outer layers through time-delayed inter-layer connections. Two types of inter-layer coupling are considered: delayed electrical synapses, which act through the spike voltage, and delayed field couplings, modeled via memristive interactions involving the flux variable. By analyzing intra- and inter-layer synchronization errors across varying coupling strengths and time delays, we explore how these factors influence synchronization performance. Our results reveal that increasing time delay generally deteriorates synchronization, with the degradation pattern depending on the coupling type. In the case of electrical synapses, synchronization loss is irregular with increasing delay, while under field coupling, the synchronization threshold rises systematically. Notably, stronger intra-layer coupling significantly mitigates the adverse effects of time delay, preserving intra-layer synchronization even at high delay values. These findings highlight the importance of coupling configuration and local connectivity strength in maintaining coherent dynamics in multilayer neuronal networks subject to transmission delays.

The bidirectional gear-driven friction nanogenerator can convert mechanical energy into electrical energy through transmission system and energy acquisition technology, which is of great significance in the development of miniaturization, intelligence and greening. Therefore, this study aims to explore the relationship between the dynamic characteristics of mechanical transmission system and the mechanical energy conversion efficiency of bi-directional gear-driven friction nanogenerator system. Considering the time-varying mesh stiffness, time-varying support stiffness, transmission error, tooth side clearance and bearing clearance, the nonlinear dynamic model of the mechanical transmission system of the bidirectional gear-driven friction nanogenerator is established. The Runge Kutta method was used to solve the vibration differential equation of a mechanical transmission system, and the influence of external load excitation frequency on the dynamic characteristics of the system was analyzed. The influence mechanism of external load excitation frequency and average mesh stiffness on the mechanical energy harvesting of the system was analyzed by combining the friction nanogenerator (TENG) energy harvesting technology. There are abundant nonlinear phenomena in the mechanical transmission system of bi-directional rack-driven friction nanogenerator. With the increase of the external load excitation frequency and the average meshing stiffness, the vibration characteristics of the mechanical transmission system will experience three different motion states, the power generation of the system will increase, but the mechanical energy conversion efficiency of the system will decrease. The results show that the mechanical energy conversion efficiency can be improved and the power generation of TENG can be increased by reasonably selecting the external load excitation frequency and meshing stiffness and avoiding the unstable region.

This paper presents a novel four-dimensional (4D) chaotic system exhibiting parametric symmetry breaking and multistability. Through equilibrium stability analysis, attractor reconstruction, Lyapunov Exponent spectra (LEs), and bifurcation diagrams, we reveal a continuous transition from symmetric period attractors to asymmetric chaotic states and rich dynamical behaviors. Additionally, considering the potential of this system in practical applications, a feedback control simulation circuit is designed and implemented to ensure its stability and effectiveness under real-world conditions. Finally, among various control strategies, this paper proposes an innovative Fixed-Time Sliding Mode Synchronization (FTSMS) strategy, determines its synchronization convergence time, and provides an important theoretical foundation for the practical application of the system.

Carbon nanotubes (CNTs) are pivotal components in nanoelectromechanical applications. Investgaing the dynamics of CNTs helps in expanding our understanding of their mechanical properties in nanoengineering endeavors. This study delves into the chaotic characteristic of single-walled carbon nanotube (SWCNT) systems involving phase-shifting external excitation and cubic nonlinear damping. Employing compactification theory, we investigate the system's dynamics at infinity, unveiling its global structure. Analytic solutions for homoclinic/heteroclinic orbits are derived, and utilizing the Melnikov method, we establish criteria for chaos onset in this periodically excited, perturbed SWCNT system. Through bifurcation diagrams, Lyapunov exponent spectra, Poincar & eacute; sections, and homoclinic bifurcation surfaces, we empirically confirm the occurrence of chaos, substantiating our theoretical analyses with simulation results.

This study examines how the temporal structure of network couplings affects synchronization, a fundamental phenomenon in numerous real-world systems. Focusing on blinking networks, a class of time-varying networks where couplings periodically switch on and off, we compare two distinct blinking schemes across three canonical dynamical systems: the Hindmarsh–Rose, Lorenz, and Rössler systems. Using the Master Stability Function (MSF) framework, we reveal a striking contrast in synchronization behavior. When all couplings are activated simultaneously during the same portion of the blinking period, the system’s synchronization stability remains unaffected by the blinking frequency, closely resembling that of an averaged static network characterized by a linear MSF profile. In contrast, when couplings are activated sequentially within each blinking period, this linear MSF pattern emerges only at high blinking frequencies (fast blinking). At lower frequencies (slow blinking), the MSF exhibits diverse, system-specific patterns. Notably, the linear MSF pattern ensures the emergence of synchronization irrespective of the underlying structural properties. Thus, these findings offer new insights into how the temporal organization of couplings governs collective dynamics in time-varying networks, particularly in contexts where the emergence and stability of synchronization are critical.

A chimera state represents a distinct configuration within interconnected oscillatory networks comprising both coherent and incoherent oscillators. In specific scenarios, multiple sets of synchronized systems can coexist, forming what is termed a multi-chimera state. This phenomenon has previously been documented in a network of FitzHugh–Nagumo systems under strong coupling conditions. In this study, we explore the impact of higher order interactions on the manifestation of multi-chimera states and their respective domains. The assessment involves utilizing measures of incoherence and discontinuity. The findings indicate that higher order networks are more prone to exhibiting multi-chimera states. Additionally, complete coherence is achieved with lower first-order coupling strength. Furthermore, the higher order network displays instances of imperfect chimera and imperfect synchronization.

There are numerous studies on Hopfield neural networks with electromagnetic induction using memristors in either autaptic or synaptic connections. In this study, we explore a novel scenario where all connections are influenced by electromagnetic induction. We investigate and compare the network’s dynamics with one memristive autapse, two memristive autapses, and a memristive synapse. The results indicate that having two memristive autapses instead of one increases the dynamical range, leading to chaotic dynamics in unequal autaptic strengths. In contrast, in the presence of the memristive synapse, chaos can emerge only in very strong synaptic strength. Using fractional-order derivatives can transform the periodic attractor of the integer-order model into a chaotic one in some parameters. Furthermore, incorporating more memristors leads to chaos at lower fractional orders.

To analyze the vibration characteristics of the electromechanical coupling transmission system of electrical vehicles under gear faults, an electromechanical coupling transmission system including two-stage meshing gear and motor system is established. Combining the effects of backlash, transmission error, and time-varying mesh stiffness on the system, the dynamic model of the transmission system includes electromechanical coupling for electrical vehicles is established by using torque as a link between mechanical and electrical systems. The meshing stiffness calculation of different fault extent is introduced to explore the nonlinear vibration characteristics of the transmission system under various faults. The vibration characteristics of systems are analyzed under different rotational speeds, impact loads, and FTP (Federal Test Procedure) actual road conditions. The results show that the cracked gear generates periodic pulses, and its vibration amplitude increases with the extent of crack. Under the same crack extent, the vibration amplitude decreases with the increase of rotational speed and impact load. At the same time, the current receives the same periodic pulse.

Gear cracks may occur during the operation of planetary driveline, leading to a huge safety hazard. However, few studies have been conducted to investigate the influence mechanism of planetary driveline vibration with crack extension. In order to simulate the actual working conditions, a damage dynamics model of the planetary gear train is constructed. Firstly, the system dynamics differential equations are established based on the dynamics model and solved to obtain the bifurcation diagram, time-domain diagram, phase diagram, three-dimensional wavelet diagram, three-dimensional spectrogram, and meshing force diagram of the system to investigate the effects of the excitation frequency and the degree of cracking of the gears on the vibration characteristics of the system. Then, the global bifurcation diagram of the system is constructed by using the cell mapping method, and the evolution mechanism of the global vibration characteristics of the system is explored according to the coexisting states of the system. In addition, the proposed dynamics model is verified by planetary gear train failure simulation experiments. The results show that the system has similar global characteristics under healthy operating conditions and cracked faults, and the system instability increases with the gear crack extension. Therefore, it is valuable to predict the planetary gear life by analysing the global vibration characteristics of the system.

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.

Investigating the functional connectivities in the brain networks of individuals with attention deficit hyperactivity disorder (ADHD) has long intrigued researchers. ADHD individuals have defects in recognizing others’facial emotions, resulting in inappropriate social interactions. While great attention has been paid to examining the pairwise interactions between various brain regions in individuals with ADHD, further exploration is required to investigate the impact of simultaneous interactions involving more than two brain regions on ADHD. To fill this research gap, the higher-order interactions of the brain networks of ADHD and healthy boys while observing facial emotions are analyzed in this study. Weighted brain hyper-networks are constructed based on the maximum cliques of the brain networks as hyperlinks. The statistical analysis of topological features extracted from the boys’brain hyper-networks revealed significant differences (P-values < 0.05) between the ADHD and healthy groups in the frontal, right temporal, and occipital brain regions. These findings may represent the defects in the higher-order interactions of brain networks in ADHD boys while processing facial images, emotions, and vision. It is hoped this study can help us gain an understanding of the complicated behavior of brain networks under the influence of ADHD.

The inescapable presence of time delay in numerous real-world systems, particularly in neuronal networks, prompts an exploration of its impact on synchronization dynamics. This study employs memristive Chialvo maps to capture the local dynamics of network nodes, while connections are homogeneously described by a linear diffusive function—referred to as electrical couplings in mathematical neuroscience—incorporating a specific time delay. Using Master stability functions (MSFs), analytical assessments are conducted to examine the stability of synchronous solutions, a validation supported by time-averaged synchronization error calculations. This research reveals the time delay's influence on the synchrony, making the synchronous state dependent on the coupling parameter's strength. The behavior of the synchronization manifold is systematically probed across synchronous and asynchronous regions analyzed by the MSF analysis. Lastly, an investigation involving a neuronal network with a global coupling configuration reveals that neurons have a tendency to organize into clusters with distinct time lags.