Synchronization Dynamics Research Articles

Effects of coupling on extremely multistable fractional-order systems

Multistability is a phenomenon in which a dynamical system possesses multiple attractors within the same set of parameters. This study explores the effects of coupling on the dynamics of a recently introduced 2D single-neuron neural network model. The system is in its original form bistable, but its extension to include fractional-order derivatives yields an unprecedented level of complexity that is characterized by extreme multistability. We provide a comprehensive analysis of the behavior of this system when coupled. We find a diverse range of attractors for two coupled systems emerging from different initial conditions, and we elucidate the transition from periodic to chaotic behavior as the coupling strength increases. We also show that the synchronization dynamics in this case ranges from anti-phase synchronization under weak coupling to complete synchronization under stronger coupling. Finally, we study the collective behavior of several coupled extremely multistable fractional-order systems, which compared to bistable systems exhibit more complexity and uncertainty as they oscillate between different attractors, or even between emerging attractors.

MEMS Electrostatically Driven Coupled Beam Filter Banks.

MEMS bandpass filters based on electrostatically driven, mechanically coupled beams with in-plane motion have been demonstrated up to the VHF band. Filters higher than second order with parallel plate drives have inherent tuning difficulties, which may be resolved by adding mass-loaded beams to the ends of the array. These beams deflect for DC voltages, and thus allow synchronized electrostatic tuning, but do not respond to in-band AC voltages and hence do not interfere with dynamic synchronization. Additional out-of-band responses may be damped, leaving the desired response. The principle is extended here to close-packed banks of filters, with adjacent arrays sharing mass-loaded beams that localize modes to sub-arrays. The operating principles are explained using a lumped element model (LEM) of the equations of motion in terms of resonant modes and the reflection of acoustic waves at discontinuities. Performance is simulated using the LEM and verified using the more realistic stiffness matrix method (SMM) for banks of up to eight filters. Similar or dissimilar filters may be combined in a compact arrangement, and the method may be extended to higher order resonances and alternative coupled resonator systems.

Experimental demonstration of coupled differential oscillator networks for versatile applications.

Oscillatory neural networks (ONNs) exhibit a high potential for energy-efficient computing. In ONNs, neurons are implemented with oscillators and synapses with resistive and/or capacitive coupling between pairs of oscillators. Computing is carried out on the basis of the rich, complex, non-linear synchronization dynamics of a system of coupled oscillators. The exploited synchronization phenomena in ONNs are an example of fully parallel collective computing. A fast system's convergence to stable states, which correspond to the desired processed information, enables an energy-efficient solution if small area and low-power oscillators are used, specifically when they are built on the basis of the hysteresis exhibited by phase-transition materials such as VO2. In recent years, there have been numerous studies on ONNs using VO2. Most of them report simulation results. Although in some cases experimental results are also shown, they do not implement the design techniques that other works on electrical simulations report that allow to improve the behavior of the ONNs. Experimental validation of these approaches is necessary. Therefore, in this study, we describe an ONN realized in a commercial CMOS technology in which the oscillators are built using a circuit that we have developed to emulate the VO2 device. The purpose is to be able to study in-depth the synchronization dynamics of relaxation oscillators similar to those that can be performed with VO2 devices. The fabricated circuit is very flexible. It allows programming the synapses to implement different ONNs, calibrating the frequency of the oscillators, or controlling their initialization. It uses differential oscillators and resistive synapses, equivalent to the use of memristors. In this article, the designed and fabricated circuits are described in detail, and experimental results are shown. Specifically, its satisfactory operation as an associative memory is demonstrated. The experiments carried out allow us to conclude that the ONN must be operated according to the type of computational task to be solved, and guidelines are extracted in this regard.

Processing of the same narrative stimuli elicits common functional connectivity dynamics between individuals

It has been suggested that conscious experience is linked to the richness of brain state repertories, which change in response to environmental and internal stimuli. High-level sensory stimulation has been shown to alter local brain activity and induce neural synchrony across participants. However, the dynamic interplay of cognitive processes underlying moment-to-moment information processing remains poorly understood. Using naturalistic movies as an ecological laboratory model of the real world, here we investigate how the processing of complex naturalistic stimuli alters the dynamics of brain network interactions and how these in turn support information processing. Participants underwent fMRI recordings during movie watching, scrambled movie watching, and resting. By measuring the phase-synchrony between different brain networks, we analyzed whole-brain connectivity patterns. Our finding revealed distinct connectivity patterns associated with each experimental condition. We found higher synchronization of brain patterns across participants during movie watching compared to rest and scrambled movie conditions. Furthermore, synchronization levels increased during the most engaging parts of the movie. The synchronization dynamics among participants were associated with suspense; scenes with higher levels of suspense induced greater synchronization. These results suggest that processing the same high-level information elicits common neural dynamics across individuals, and that whole-brain functional connectivity tracks variations in processed information and subjective experience.

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

General Methods to Synchronize Fractional Discrete Reaction–Diffusion Systems Applied to the Glycolysis Model

Because they are useful for both enabling numerical simulations and containing well-defined physical phenomena, discrete fractional reaction–diffusion models have attracted a great deal of interest from academics. Within the family of fractional reaction–diffusion models, a discrete form is examined in detail in this study. Furthermore, we investigate the complex synchronization dynamics of a suggested discrete master–slave reaction–diffusion system using the accuracy of linear control techniques combined with a fractional discrete Lyapunov approach. This study’s deviation from the behavior of equivalents with integer orders makes it very fascinating. Like the non-local nature inherent in Caputo fractional derivatives, it creates a memory Lyapunov function that is closely linked to the historical background of the system. The investigation provides a strong basis to the theoretical results.

Quantum synchronization with correlated baths

We study quantum synchronization under the nonequilibrium reservoirs. We consider a two-qubit XXZ chain coupled independently to their own reservoirs modeled by the collisional model. Two reservoir particles, initially prepared in a thermal state or a state with coherence, are correlated through a unitary transformation and afterward interact locally with the two quantum subsystems. We study the quantum effect of reservoir on synchronous dynamics of system. By preparing different reservoir initial states or manipulating the reservoir particles coupling and the temperature gradient, we find that quantum entanglement of reservoir is the key to control quantum synchronization of system qubits.

Synchronization of delayed coupled neurons with multiple synaptic connections.

Synchronization is a key feature of the brain dynamics and is necessary for information transmission across brain regions and in higher brain functions like cognition, learning and memory. Experimental findings demonstrated that in cortical microcircuits there are multiple synapses between pairs of connected neurons. Synchronization of neurons in the presence of multiple synaptic connections may be relevant for optimal learning and memory, however, its effect on the dynamics of the neurons is not adequately studied. Here, we address the question that how changes in the strength of the synaptic connections and transmission delays between neurons impact synchronization in a two-neuron system with multiple synapses. To this end, we analytically and computationally investigated synchronization dynamics by considering both phase oscillator model and conductance-based Hodgkin-Huxley (HH) model. Our results show that symmetry/asymmetry of feedforward and feedback connections crucially determines stability of the phase locking of the system based on the strength of connections and delays. In both models, the two-neuron system with multiple synapses achieves in-phase synchrony in the presence of small and large delays, whereas an anti-phase synchronization state is favored for median delays. Our findings can expand the understanding of the functional role of multisynaptic contacts in neuronal synchronization and may shed light on the dynamical consequences of pathological multisynaptic connectivity in a number of brain disorders.

Adaptability of water resources development and utilization to social-economy system in Hunan province, China

The interplay of water resources with social-economy spheres involves a reciprocal feedback mechanism. With the acceleration of the construction process of modernized water networks in Hunan Province, investigating the adaptation status of the "Water-Social-Economy " composite system (WSE) is crucial for promoting sustainability. This study clarifies the connotation of the adaptability of WSE, and the quantitative analyses were conducted through coupling coordinative degree, harmonious development capacity, and the evolution of development lag types among the 14 cities of Hunan Province from 2005 to 2020. The results show that: (1) The development index of the water resources subsystem (WRS) showed a “downward-fluctuation-upward” trend, while the development index of the social-economy subsystem (SES) showed signs of great improvement, the former didn’t catch up with the latter. (2) The coupling coordination degree of WSE developed well, and reached the coordinative development stage by 2020, but the unbalanced spatial pattern between north to south and east to west still exists and is further intensified. (3) The development ability of WSE improved while the harmony ability reduced, and the development rate of WRS and SES hasn’t achieved dynamic synchronization. Finally, the policies and suggestions to improve the adaptability are put forward, which is of instructive significance for the sustainable development of water suitability.

The geometry of synchronization: quantifying the coupling direction of physiological signals of stress between individuals using inter-system recurrence networks.

In the study of synchronization dynamics between interacting systems, several techniques are available to estimate coupling strength and coupling direction. Currently, there is no general 'best' method that will perform well in most contexts. Inter-system recurrence networks (IRN) combine auto-recurrence and cross-recurrence matrices to create a graph that represents interacting networks. The method is appealing because it is based on cross-recurrence quantification analysis, a well-developed method for studying synchronization between 2 systems, which can be expanded in the IRN framework to include N > 2 interacting networks. In this study we examine whether IRN can be used to analyze coupling dynamics between physiological variables (acceleration, blood volume pressure, electrodermal activity, heart rate and skin temperature) observed in a client in residential care with severe to profound intellectual disabilities (SPID) and their professional caregiver. Based on the cross-clustering coefficients of the IRN conclusions about the coupling direction (client or caregiver drives the interaction) can be drawn, however, deciding between bi-directional coupling or no coupling remains a challenge. Constructing the full IRN, based on the multivariate time series of five coupled processes, reveals the existence of potential feedback loops. Further study is needed to be able to determine dynamics of coupling between the different layers.

Initial condition-offset regulating synchronous dynamics and energy diversity in a memristor-coupled network of memristive HR neurons

Memristors can be thought of as special connection synapses with internal states that regulate synchronous behavior or energy propagation between neurons in a neural network. By connecting two memristive Hindmarsh-Rose (mHR) neurons with one memristor coupling, this paper synthesizes a memristor-coupled mHR neuron (MC-mHRN) network without equilibrium point. For this network, the synchronization condition regulated by the initial condition-offset (ICO) of the memristive channel are derived theoretically, and the ICO-regulating synchronous dynamics is evaluated numerically. Furthermore, the Hamiltonian energy of mHR neuron is studied by Helmholtz's theorem, and the ICO-regulating energy diversity is analyzed numerically. It is demonstrated that the coupling strength and initial condition of the memristive channel can regulate the synchronous dynamics and energy diversity in the MC-mHRN network, thus achieving complete synchronization as well as energy balance. Consequently, the two mHR neurons in hidden chaotic firing modes deliver field energy via memristive channel until the fully synchronized energy balance is achieved. In addition, a digital platform of the MC-mHRN network is fabricated, and the experimental results validate the numerical ones of the synchronous dynamics.

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

This paper addresses the challenge of synchronizing the dynamics of two distinct 3D chaotic systems, specifically the Rabinovich and Rabinovich-Fabrikant systems, employing a finite-time synchronization approach. These chaotic systems exhibit diverse characteristics and evolving chaotic attractors, influenced by specific parameters and initial conditions. Our proposed low-cost finite-time synchronization method leverages the signum function's tracking properties to facilitate controlled coupling within a finite time frame. The design of finite-time control laws is rooted in Lyapunov stability criteria and lemmas. Numerical experiments conducted within the MATLAB simulation environment demonstrate the successful asymptotic synchronization of the master and slave systems within finite time. To assess the global robustness of our control scheme, we applied it across various system parameters and initial conditions. Remarkably, our results reveal consistent synchronization times and dynamics across these different scenarios. In summary, this study presents a finite-time synchronization solution for non-identical 3D chaotic systems, showcasing the potential for robust and reliable synchronization under varying conditions.

Dynamical analysis and synchronization control of flux-controlled memristive chaotic circuits and its FPGA-Based implementation

This paper focuses on addressing the synchronization control problem of memristive chaos through the investigation of a single feedback controller strategy. Our objective is to deploy this strategy on field-programmable gate arrays (FPGA) with the aim of bolstering the security and reliability of memristive chaotic synchronization control. Concurrently, we seek to enhance system performance and fulfill the diverse requirements of various applications. Initially, the study utilizes chaos synchronization theory and the Routh–Hurwitz stability criterion to devise a feedback controller with a single input. This controller plays a crucial role in establishing a synchronization system specifically designed for memristive chaos. Subsequently, the FPGA design approach utilizing DSP Builder is employed to create models for both the single-input feedback controller and the memristive chaotic synchronization control system. This approach facilitates the efficient translation of these theoretical concepts into practical digital circuit implementations. Finally, the paper concludes with an experimental analysis that verifies the feasibility and practical applicability of the FPGA circuit design for memristive chaotic synchronization control.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition.

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

Noisy image segmentation based on synchronous dynamics of coupled photonic spiking neurons.

The collective dynamics in neural networks is essential for information processing and has attracted much interest on the application in artificial intelligence. Synchronization is one of the most dominant phenomenon in the collective dynamics of neural network. Here, we propose to use the spiking dynamics and collective synchronization of coupled photonic spiking neurons for noisy image segmentation. Based on the synchronization mechanism and synchronization control, the noised pattern segmentation is demonstrated numerically. This work provides insight into the possible application based on the collective dynamics of large-scale photonic networks and opens a way for ultra-high speed image processing.

Analytical phase reduction for weakly nonlinear oscillators

Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to few systems. In this work, we analytically perform phase reduction for a wide class of oscillators by extending the Poincaré–Lindstedt perturbation theory. We exemplify the utility of our approach by analyzing an ensemble of Van der Pol oscillators, where the derived phase model provides analytical predictions of their collective synchronization dynamics.

Dynamic event-triggered attitude synchronization of multi-spacecraft formation via a learning neural network control approach

This paper addresses the robust attitude synchronization issue in a multi-spacecraft formation system subjected to limited communication, space disturbances, modeling uncertainties, and actuator faults. To accommodate limited inter-spacecraft communication, a dynamic event-triggered mechanism is designed to reduce the communication trigger frequency by dynamically adjusting the trigger threshold. Moreover, an event-based distributed self-learning neural-network control (SLN2C) law is developed to guarantee robust attitude synchronization during multi-spacecraft formation. In the SLN2C scheme, a learning radial basis function neural network (RBFNN) model is proposed to online approximate and compensate for lumped disturbances, in which an iterative learning algorithm with a variable learning intensity is adopted to update the weight matrix of the RBFNN model. Compared with the traditional fixed learning intensity, a variable one can reduce initial oscillation and weaken the saturation response. Numerical simulations and comparisons are performed to illustrate the effectiveness and superiority of the proposed event-based spacecraft attitude synchronization control method.

Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators

Ring structures are crucial in network neuroscience, enabling the integration of neural information through closed loop circuits within feedback systems. Here, we use numerical bifurcation analysis to explore time delay effects on a ring of delay-coupled Wilson–Cowan masses. Investigating a low-dimensional ‘self-coupled’ version of the aforementioned system, we uncover the bifurcation structure of the synchronization manifold, and unveil a diverse array of dynamic synchronization patterns that emerge as a consequence of Hopf branch crossings and subsequent higher-order bifurcations. Analysis of the full system reveals transverse instabilities in the synchronized state for large regions of parameter space, with the ring network architecture promoting various dynamics depending on the balance between coupling strength and delay time. Under weak coupling, emergent oscillations are generally synchronous or anti-phase synchronous, with transitions between them triggered by a torus bifurcation of a periodic orbit. Regions of synchronous and anti-phase synchronous solutions are delineated by weakly chaotic borders due to the breakdown of the torus. As coupling strength increases, the bifurcation diagram displays more overlapped branching structure, resulting in increasingly complicated, multistable dynamics.

Quantum effects on the synchronization dynamics of the Kuramoto model

Quantum effects on the synchronization dynamics of the Kuramoto model

A high‐efficiency frequency synchronization scheme for low Earth orbit satellite communications based on dynamic game theory

SummaryThe rapid development of satellite internet networks has given rise to a new vision for the sixth generation of networking technology. However, the Doppler effect is relatively serious in satellite internet networks because a satellite moves quickly relative to a ground terminal. Therefore, there is an urgent need to study intelligent and dynamic synchronization methods to solve the problem of the rapidly changing Doppler frequency offset. Traditional methods do not consider the impact of spatial changes and typically focus on enhancing the estimation range or accuracy. We analyze various scenarios under phased array beam hopping and establish constraints between the terminal location, satellite ephemeris, subsatellite point track, elevation angle, and carrier frequency offset. We introduce dynamic game theory into frequency synchronization to optimize multiple Doppler estimation performance under rapidly changing channel conditions. We take the combination of carrier frequency offset estimation algorithm strategies at the current moment as the game entity. Simulation results demonstrate that the proposed method can achieve an estimation accuracy of 100 Hz and an estimation range of ±800 kHz. During the onboard test, the probability of achieving complete synchronization (when the synchronization success rate is 1) is 0.65, which is much higher than the 0.15 of the single method.