Synchronization Phenomena Research Articles

Intermittent-like synchronization and desynchronization phenomena in a Colpitts network model.

This study investigates the dynamics of a modified Colpitts oscillator, exhibiting complex periodic and chaotic behaviors. Our research explores the dynamics and synchronization of coupled chaotic Colpitts oscillators, crucial for understanding their potential applications and behaviors. The main discovery is the emergence of a phase in which the systems achieve either complete synchronization or desynchronization. This behavior depends on the values of the coupling parameter. The subsequent challenge involves understanding how the coupling parameter influences the emergence of this synchronization phenomenon.

Synchronization in a higher-order neuronal network with blinking interactions

The synchronization of higher-order networks presents a fascinating area of exploration within nonlinear dynamics and complex networks. Simultaneously, growing research interest focuses on uncovering synchronization dynamics in time-varying networks with time-dependent coupling structures, reflecting their prevalence in real-world systems like neuronal networks. Motivated by this, the present study delves into the synchronization phenomenon within a higher-order network incorporating a blinking coupling scheme. Blinking coupling is an on–off switching coupling that has been demonstrated to enhance synchronization effectively. Its efficacy stems from ensuring synchronization, as the master stability function (MSF) follows a linear pattern. In this study, our objective is to investigate such a time-varying coupling scheme in a higher-order network configuration. We investigate the influence of coupling parameters and blinking frequency on synchronization behavior. Notably, our findings demonstrate that as the blinking frequency increases, the network exhibits a gradual convergence toward the behavior of the average network. Furthermore, leveraging the analytical framework of MSF and the average synchronization error, we provide analytical and numerical evidence confirming that the MSF pattern within the average network transforms into a linear function. The synchronous and asynchronous regions also exhibit a clear separation demarcated by a linear curve across the coupling parameter space. Moreover, our results suggest that incorporating higher-order interactions fosters enhanced synchrony by effectively scaling the synchronization patterns to lower coupling parameter values.

Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies.

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.

Phenomenon of self-oscillation in bubble dynamics: Bouncing acoustic bubbles

Self-oscillations underlie many natural phenomena, such as heartbeat, ocean waves, and the pulsation of variable stars. From pendulum clocks to the behavior of animal groups, self-oscillation is one of the keys to the understanding of synchronization phenomena and hence to the collective behavior of interacting systems. In this study, we consider two closely spaced bubbles pulsating in the kHz range in response to ultrasonic excitation. A translational bouncing motion emerges from their interaction with a much lower frequency than the bubble pulsation frequency. Our analysis reveals that the observed bubble bouncing exhibits the main features of self-oscillation, such as negative damping and the emergence of a limit cycle. These results highlight unexpected nonlinear effects in the field of microbubbles and give insights into the understanding of synchronization in large bubble clouds.

Dynamic Analysis of a Simple Cournot Duopoly Model Based on a Computed Cost

The paper is organized to study some mathematical properties and dynamics of a simple Cournot duopoly game based on a computed quadratic cost. The time evolution of this game is described by a two-dimensional noninvertible discrete time map using the bounded rationality mechanism. For this map, some dynamic characteristics such as multistability and synchronization are investigated. Its equilibrium points are obtained for the asymmetric case, and their conditions of stability are obtained. Our results investigate that the Nash equilibrium point may be unstable due to flip bifurcation and under certain parameter values, and Neimark–Sacker bifurcation is born after the period-4 cycle. Through some restrictions, the coordinate axes of the map construct an invariant manifold, and therefore, their dynamics can be analyzed by using a one-dimensional map. In the symmetric case, both firms behave identically, and this implies that the diagonal set forms an invariant manifold, and hence the synchronization phenomena take place. Furthermore, the global bifurcation of the map is confirmed through contact between critical curves and the boundaries of infeasible domains.

Observer‐based hybrid triggered control design for cluster synchronization of nonlinear complex dynamical networks

SummaryThe issues of cluster synchronization and state estimation for a class of nonlinear complex dynamical networks are concurrently focused in this study. In precise, led by the design of complex dynamical networks, a proportional integral‐based observer is implemented for achieving robustness, by the virtue of which the states of examined networks are estimated. Thereupon, a proportional integral observer‐based hybrid triggered control scheme is proposed, wherein, the switch‐over between time‐ and event‐ triggered scheme is governed through a Bernoulli distributed random variable. Further, with the application of mixed and passivity performance technique, the external disturbances for the addressed complex dynamical networks are reduced. Based on the Lyapunov stability theory, the requisite sufficient conditions in respect of linear matrix inequalities are provided which ensures the discussed complex dynamical network's synchronization phenomenon. In a further, the presented criteria are exploited for the attainment of required controller, proportional and integral gain matrices. In conclusion, the applicability of proposed results and efficacy of the undertaken strategy are evidently proven with the illustration of two numerical examples with Chua's circuit and Goodwin oscillator model.

Biophysical modulation and robustness of itinerant complexity in neuronal networks.

Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability in the inhibitory population. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.

Metronome synchronization in the presence of friction

This study investigates the synchronization phenomenon inherent to mechanical metronomes. Synchronization properties were probed under diverse conditions, with modifications to parameters such as the number of metronomes, the tabletop material, the additional weight on the platform, and the friction coefficient between the roller and platform. Experimental outcomes demonstrate that the synchronization is significantly influenced by the platform's movement, which is subsequently determined by the properties of both the platform and roller. An analytical modeling approach provided insights into these effects, particularly when analyzing two metronomes placed on a flat platform equipped with rollers. Central to the findings is the revelation that both the coefficient of friction and the mass of supplementary weights play crucial roles in shaping synchronization behavior, a conclusion in line with experimental observations. The numerical segment of the study leveraged the Kuramoto model. Observations centered on the phase variation of resonators and a time-responsive order parameter, shedding light on the role of coupling strength in synchronization and its absence. Overall, this study furnishes a thorough theoretical and experimental exploration of mechanical metronome synchronization, targeting an enhanced understanding and application of the observed phenomenon.

Contingency and Synchronization: Conceptual Framework, Artistic Experiments and Speculative Syn-theses

Contingency and Synchronization is an ongoing research project exploring the interplay between openness and predictability in computational art. Utilizing distributed multi-agent networks, the project investigates computational synchronization phenomena across installations and visualizations. Central to the project are the concepts of contingency and synchronization, providing a framework for understanding aesthetic nuances arising from computation, sound, site, and collaborative decision-making. This paper examines the project’s conceptual and artistic impact. It explores the relationship between contingency and synchronization and addresses repercussions for concepts of listening, emergence, computation, space, and performance, and presents speculative theses outlining preliminary findings.

Synchronization phenomena in thermoelastic waves connected in parallel

In this paper, the phenomenon of synchronization in nonlinearly coupled thermoelastic waves is investigated. The existence of a finite-dimensional smooth global attractor A α is proven in the natural energy space, where α is the coupling parameter. It is also proved that the coupled thermoelastic wave system can be reduced to a single thermoelastic wave when α tends to infinity. Subsequently, the upper-semicontinuity of their attractors is proven as α → ∞ . These results are ultimately employed to establish the synchronization phenomena for coupled thermoelastic waves. To the best of our knowledge, the synchronization of thermoelastic waves has not been considered before.

Conflict-free joint decision by lag and zero-lag synchronization in laser network

With the end of Moore’s Law and the increasing demand for computing, photonic accelerators are garnering considerable attention. This is due to the physical characteristics of light, such as high bandwidth and multiplicity, and the various synchronization phenomena that emerge in the realm of laser physics. These factors come into play as computer performance approaches its limits. In this study, we explore the application of a laser network, acting as a photonic accelerator, to the competitive multi-armed bandit problem. In this context, conflict avoidance is key to maximizing environmental rewards. We experimentally demonstrate cooperative decision-making using zero-lag and lag synchronization within a network of four semiconductor lasers. Lag synchronization of chaos realizes effective decision-making and zero-lag synchronization is responsible for the realization of the collision avoidance function. We experimentally verified a low collision rate and high reward in a fundamental 2-player, 2-slot scenario, and showed the scalability of this system. This system architecture opens up new possibilities for intelligent functionalities in laser dynamics.

Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields.

Self-oscillating coupled systems possess the ability to actively absorb external environmental energy to sustain their motion. This quality endows them with autonomy and sustainability, making them have application value in the fields of synchronization and clustering, thereby furthering research and exploration in these domains. Building upon the foundation of thermal responsive liquid crystal elastomer-based (LCE-based) spring oscillators, a synchronous system comprising three LCE-based spring oscillators interconnected by springs is established. In this paper, the synchronization phenomenon is described, and the self-oscillation mechanism is revealed. The results indicate that by varying system parameters and initial conditions, three synchronization patterns emerge, namely, full synchronous mode, partial synchronous mode, and asynchronous mode. For strongly interacting systems, full synchronous mode always prevails, while for weak interactions, the adjustment of initial velocities in magnitude and direction yields the three synchronization patterns. Additionally, this study explores the impact of several system parameters, including LCE elasticity coefficient and spring elasticity coefficient, on the amplitude, frequency, and synchronous mode of the system. The findings in this paper can enhance our understanding of the synchronization behavior of multiple mutually coupled LCE-based spring oscillators, with promising applications in energy harvesting, soft robotics, signal monitoring, and various other fields.

Analysis of a degenerate reaction–diffusion anthrax model with spatial heterogeneity

To investigate the impact of spatial heterogeneity on anthrax transmission, we develop a novel degenerate reaction–diffusion model for anthrax. Despite the lack of compactness of the solution map, the asymptotic smoothness is confirmed by examining its contractility. We establish two thresholds, s(J) obtained by an auxiliary system and R0 defined by next generation operator, corresponding to the extinction and persistence of anthrax, respectively. Additionally, we investigate the steady-state bifurcation at the disease-free equilibrium by bifurcation theory. Our numerical simulations reveal the effects of heterogeneity on the transmission of anthrax and discover a phenomenon of spatial synchronization, which maintains the invariance of the basic reproduction number. Notably, we demonstrate that synchronization is the underlying mechanism for this invariance. In summary, our findings provide valuable insights for advancing the understanding of infectious disease transmission dynamics.

Stationary equilibria and their stability in a Kuramoto MFG with strong interaction

Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game (MFG) version of the classical Kuramoto model, which describes synchronization phenomena in a large population of “rational” interacting oscillators. The MFG model exhibits several stationary equilibria, but the characterization of these equilibria and their ability to capture dynamic equilibria in long time remains largely open. In this paper, we demonstrate that, up to a phase translation, there are only two possible stationary equilibria: the incoherent equilibrium and the self-organizing equilibrium, given that the interaction parameter is sufficiently large. Furthermore, we present some local stability properties of the self-organizing equilibrium.

Model of Satellite Communication Channel Functioning under Conditions of Episodic Synchronization with Pulse Interference Flows

The article investigates the effect of pulse interference on information reception in conditions of episodic synchronization of frames of the physical level of a satellite communication channel with streams of radio pulses of unintended interference. An analytical model of the influence of pulse interference on the reception of information in a satellite communication channel under conditions of episodic synchronization of physical-level frames with pulse interference streams is proposed. Using the example of the DVB family of standards, the combined effect of noise and unintended impulse interference on the conditional error probabilities when receiving a synchro group, the service part of the header and the information part of the frame is shown. Estimates of the average number of frames of the physical level for the duration of the interval of episodic synchronization, the number of intervals of episodic synchronization and the proportion of elementary parcels in the frame exposed to interference, depending on the duration of the pulse interference, are given. It is shown that there are such relations between the duration of the interference pulse and the continuity of the sequence, in which the phenomenon of the episodic synchronization of physical-level frames with the flow of pulse interference has a significant impact on the functioning of the satellite communication channel. The dependences of the probability of erroneous reception of a frame of the physical level of a satellite communication channel on the signal-to-interference ratio at the fixed signal-to-noise ratio and on the duration of the interference pulse are obtained. It has been found that at high signal-to-noise ratios and the duration of the interference correlated with the duration of the service part of the frame, but significantly less than the duration of the frame, the probability of erroneous reception of the frame may be higher than at lower signal-to-noise ratios due to errors when receiving the service part of the frames.

UNVEILING THE MYSTERY OF NEURONAL SYNCHRONIZATION: HOW COORDINATED BRAIN ACTIVITY SHAPES COGNITION IN THE CONTEXT OF EDUCATION

Neuronal synchronization, a captivating and intricate phenomenon within the realm of neuroscience, unfolds as a mesmerizing dance of coordinated firing among groups of neurons, ultimately giving rise to distinctive brain rhythms. This paper embarks on a comprehensive exploration, delving into the profound impact of neuronal synchronization on cognition, particularly within the educational landscape. The journey navigates the nexus of neuroscience and education from unraveling the fundamental mechanisms underlying this phenomenon to elucidating its far-reaching cognitive consequences and practical applications in teaching. This exploration extends beyond theoretical discussions to embrace real-world applications, with case studies and examples illustrating successful implementations of neuronal synchronization principles in educational settings. These instances serve as beacons, shedding light on how understanding and leveraging neuronal synchronization can significantly enhance the teaching and learning experience. As we peer into the future, emerging trends in neuroeducation come to the forefront. This trajectory holds promise for personalized and adaptive learning experiences dynamically shaped by the principles of neuronal synchronization. The potential benefits of inclusive education become apparent, emphasizing the importance of recognizing and accommodating the diverse cognitive profiles of learners. In essence, this paper positions neuronal synchronization not merely as a scientific concept but as a guiding principle poised to revolutionize pedagogy. The intricate interplay between neuroscience and education showcased through the lens of neuronal synchronization, beckons a future where scientific insights do not just inform teaching strategies intricately woven into the fabric of our cognitive processes. This abstract invites readers to embark on a journey that transcends disciplinary boundaries, illuminating the transformative potential that understanding neuronal synchronization holds for the evolution of education.

Time-Frequency-Space EEG Decoding Model Based on Dense Graph Convolutional Network for Stroke.

Stroke, a sudden cerebrovascular ailment resulting from brain tissue damage, has prompted the use of motor imagery (MI)-based Brain-Computer Interface (BCI) systems in stroke rehabilitation. However, analyzing EEG signals from stroke patients is challenging because of their low signal-to-noise ratio and high variability. Therefore, we propose a novel approach that combines the modified S-transform (MST) and a dense graph convolutional network (DenseGCN) algorithm to enhance the MI-BCI performance across time, frequency, and space domains. MST is a time-frequency analysis method that efficiently concentrates energy in EEG signals, while DenseGCN is a deep learning model that uses EEG feature maps from each layer as inputs for subsequent layers, facilitating feature reuse and hyper-parameters optimization. Our approach outperforms conventional networks, achieving a peak classification accuracy of 90.22% and an average information transfer rate (ITR) of 68.52 bits per minute. Moreover, we conduct an in-depth analysis of the event-related desynchronization/event-related synchronization (ERD/ERS) phenomenon in the deep-level EEG features of stroke patients. Our experimental results confirm the feasibility and efficacy of the proposed approach for MI-BCI rehabilitation systems.

Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model

This study investigates a structurally unstable synchronization phenomenon observed in the two-coupled Izhikevich neuron model. As the result of varying the system parameter in the region of parameter space close to where the unstable synchronization is observed, we find significant changes in the stability of its periodic motion. We derive a discrete-time dynamical system that is equivalent to the original model and reveal that the unstable synchronization in the continuous-time dynamical system is equivalent to border-collision bifurcations in the corresponding discrete-time system. Furthermore, we propose an objective function that can be used to obtain the parameter set at which the border-collision bifurcation occurs. The proposed objective function is numerically differentiable and can be solved using Newton’s method. We numerically generate a bifurcation diagram in the parameter plane, including the border-collision bifurcation sets. In the diagram, the border-collision bifurcation sets show a novel bifurcation structure that resembles the “strike-slip fault” observed in geology. This structure implies that, before and after the border-collision bifurcation occurs, the stability of the periodic point discontinuously changes in some cases but maintains in other cases. In addition, we demonstrate that a border-collision bifurcation set successively branches at distinct points. This behavior results in a tree-like structure being observed in the border-collision bifurcation diagram; we refer to this structure as a border-collision bifurcation tree. We observe that a periodic point disappears at the border-collision bifurcation in the discrete-time dynamical system and is simultaneously replaced by another periodic point; this phenomenon corresponds to a change in the firing order in the continuous-time dynamical system.

Urban cybernotopics: The flow pattern

At the beginning of the 21st century the world has moved into the phase of global restructuring characterised by large-scale crises of life organization and science. For any science it is important to investigate the methodology of its cognition. Architecture and urban planning are no exception. The current commercial and industrial civilisation is built upon Western European positivism based on individualism, for which it is important how phenomena occur, not why they occur. The alternative to such a vision is a cosmic worldview based on the search for a genetic, eternal and always consistent connection between humans and nature in the space of the biosphere. The current instrumental and technical progress should be replaced by an organic progress that considers man and nature in a single connected Co-existence. This approach dictates a new urban planning in the perspective of cybernotopics, which considers the triad “nature – population – economy” as a flow pattern – the phenomenon of synchronicity in the dynamic, changeable, mobile equilibrium in the space of the biosphere. The technical external process of the impact on nature should be replaced by an organic process.

Synchronization and Clustering in Complex Quadratic Networks.

Synchronization and clustering are well studied in the context of networks of oscillators, such as neuronal networks. However, this relationship is notoriously difficult to approach mathematically in natural, complex networks. Here, we aim to understand it in a canonical framework, using complex quadratic node dynamics, coupled in networks that we call complex quadratic networks (CQNs). We review previously defined extensions of the Mandelbrot and Julia sets for networks, focusing on the behavior of the node-wise projections of these sets and on describing the phenomena of node clustering and synchronization. One aspect of our work consists of exploring ties between a network's connectivity and its ensemble dynamics by identifying mechanisms that lead to clusters of nodes exhibiting identical or different Mandelbrot sets. Based on our preliminary analytical results (obtained primarily in two-dimensional networks), we propose that clustering is strongly determined by the network connectivity patterns, with the geometry of these clusters further controlled by the connection weights. Here, we first explore this relationship further, using examples of synthetic networks, increasing in size (from 3, to 4, to 20 nodes). We then illustrate the potential practical implications of synchronization in an existing set of whole brain, tractography-based networks obtained from 197 human subjects using diffusion tensor imaging. Understanding the similarities to how these concepts apply to CQNs contributes to our understanding of universal principles in dynamic networks and may help extend theoretical results to natural, complex systems.