Synchronization Phenomena Research Articles

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.

Synchronization phenomena observed in glacial–interglacial cycles simulated in an Earth system model of intermediate complexity

Abstract. The glacial–interglacial cycles of the Quaternary exhibit 41 kyr periodicity before the Mid-Pleistocene Transition (MPT) around 1.2–0.8 Myr ago and ∼ 100 kyr periodicity after that. From the viewpoint of dynamical systems, proposed mechanisms generating these periodicities are broadly divided into two types: (i) nonlinear forced responses of a mono- or multi-stable climate system to the astronomical forcing or (ii) synchronization of internal self-sustained oscillations to the astronomical forcing. In this study, we investigate the dynamics of glacial cycles simulated by the Earth system model of intermediate complexity CLIMBER-2 with a fully interactive carbon cycle, which reproduces the MPT under gradual changes in volcanic-CO2 degassing and regolith cover. We report that, in this model, the dominant frequency of glacial cycles is set in line with the principle of synchronization. It is found that the model exhibits self-sustained oscillations in the absence of astronomical forcing. Before the MPT, glacial cycles synchronize to the 41 kyr obliquity cycles because the self-sustained oscillations have periodicity relatively close to 41 kyr. After the MPT the timescale of internal oscillations becomes too long to follow every 41 kyr obliquity cycle, and the oscillations synchronize to the 100 kyr eccentricity cycles that modulate the amplitude of climatic precession. The latter synchronization occurs with the help of the 41 kyr obliquity forcing, which enables some terminations and glaciations to occur robustly at their right timing. We term this phenomenon vibration-enhanced synchronization because of its similarity to the noise-enhanced synchronization known in nonlinear science. While we interpret the dominant periodicities of glacial cycles as the result of synchronization of internal self-sustained oscillations to the astronomical forcing, the Quaternary glacial cycles show facets of both synchronization and forced response.

Synchronization of dissipatively coupled oscillators

Synchronization is common in both nature and human physiology, often used to illustrate nonlinear dynamics. Interestingly, one can initiate their comprehension of this phenomenon from pure linear systems. In this Tutorial, we begin with a theoretical exploration of coupled oscillators’ dynamic behavior, enabling us to discern and contrast the unique attributes of dissipative coupling as opposed to commonly observed coherent coupling. We then examine synchronization in two dissipative coupled linear systems: one with two pendulums mutually linked via the Lenz effect and the other with two RLC oscillators coupled via a resistor. This Tutorial is designed to serve as a concise starting point for researchers interested in exploring synchronization phenomena using a simplified model driven solely by dissipative coupling.

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.

Synchronization and chaos control in coupled Non-identical systems: application in Wind Turbine-Grid coupled power systems

The increasing number of renewable energy systems coupled to the grid can lead to electrical energy losses when the currents or voltages of the two systems are not synchronized. Many mathematical models have investigated the phenomenon of synchronization in coupled systems. Here, we mathematically model the dynamics of a wind turbine-grid coupled system as a periodically driven Duffing resonator coupled to a Van der Pol oscillator with both position and velocity coupling. We consider the fluctuating nature of the wind as the only external driving force. We integrate the coupled system of equations under different coupling strengths and driven frequencies using the Runge-Kutta method of order 4(RK4). The result suggests that synchronization can be achieved at higher coupling strengths even with small values of the driven frequencies than at lower coupling strengths. At higher values of the driven frequency, the system exhibits chaotic behavior for both strong and weak couplings but with synchronization maintained only for the strong coupling case. Our results suggest chaos and synchronization can be controlled in this system by turning appropriate parameters.

Learning algorithms for oscillatory neural networks as associative memory for pattern recognition

Alternative paradigms to the von Neumann computing scheme are currently arousing huge interest. Oscillatory neural networks (ONNs) using emerging phase-change materials like VO2 constitute an energy-efficient, massively parallel, brain-inspired, in-memory computing approach. The encoding of information in the phase pattern of frequency-locked, weakly coupled oscillators makes it possible to exploit their rich non-linear dynamics and their synchronization phenomena for computing. A single fully connected ONN layer can implement an auto-associative memory comparable to that of a Hopfield network, hence Hebbian learning rule is the most widely adopted method for configuring ONNs for such applications, despite its well-known limitations. An extensive amount of literature is available about learning in Hopfield networks, with information regarding many different learning algorithms that perform better than the Hebbian rule. However, not all of these algorithms are useful for ONN training due to the constraints imposed by their physical implementation. This paper evaluates different learning methods with respect to their suitability for ONNs. It proposes a new approach, which is compared against previous works. The proposed method has been shown to produce competitive results in terms of pattern recognition accuracy with reduced precision in synaptic weights, and to be suitable for online learning.

Multisoliton complex systems with explicit superpotential interactions

We consider scalar field theories in dimensions with N fields which interact through a potential , which is defined in terms of an explicit superpotential W. We construct W for any N in terms of a known superpotential w for a single-scalar model, such as that for the sine-Gordon equation or the ϕ 4 model, leading to an expression for V which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential W for N scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate ϕ 4 and ϕ 6 models with N scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the ϕ 6 system for N = 3.

Desynchrony induced by higher-order interactions in triplex metapopulations.

In a predator-prey metapopulation, two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a metapopulation. In this article, we study predator-prey patches that communicate with one another while being interconnected through distinct dispersal structures in the layers of a three-layer multiplex network. We investigate the synchronization phenomenon among the patches of the outer layers by introducing higher-order interactions (specifically three-body interactions) in the middle layer. We observe a decrease in the synchronous behavior or, alternatively, an increase in desynchrony due to the inclusion of group interactions among the patches of the middle layer. The advancement of desynchrony becomes more prominent with increasing strength and numbers of three-way interactions in the middle layer. We analytically validate our numerical results by performing a stability analysis of the referred synchronous solution using the master stability function approach. Additionally, we verify our findings by taking into account two distinct predator-prey models and dispersal topologies, which ultimately supports that the findings are generalizable across various models and dispersal structures.

The seasonal influenza transmission dynamic and the correlation analysis with meteorology in Beijing

Based on the transmission mechanism of seasonal influenza, this paper establishes a SEIMHRS model with hospital-visiting behavior and periodic transmission rate, and then analyzes the existence and stability of disease-free and endemic periodic solutions theoretically. Taking the epidemic of seasonal influenza during 2013–2018 in Beijing and conducting parameter estimation, we derive its basic reproduction ratio [Formula: see text] is 1.0065. Then we concentrate on the correlation between time-varying transmission rate of influenza and change pattern of three meteorology indices for the first time. The results novelly show that there exists a synchronization phenomenon between the transmission rate and variation pattern of average atmospheric pressure and that there is an anti-synchronism phenomenon between that of the average temperature. Whereas it only shows a normal phase difference with the variation pattern of relative humidity. Finally we advocate emphasis on the effect of variation trend of meteorology on influenza prediction.

Numerical investigation of combustion instability in a liquid rocket engine: Interaction effect between hydrodynamics and acoustic mode

In this paper, we present the numerical evidence of multiple bifurcations in thermoacoustic instability as we decrease the equivalence ratio (ϕ) from fuel-rich (ϕ = 1.5) to fuel-lean (ϕ =0.59) within a single-element coaxial liquid rocket engine burning hydrogen peroxide and methane. An axisymmetric compressible Large Eddy Simulation solver in an open-source platform OpenFOAM combined with a global methane chemical kinetical mechanism was used to model the turbulent mixing and combustion process. After the validation of grid independence and simulation results, the synchronization phenomenon between hydrodynamic instability, acoustics and combustion is the main focus of this paper. The results here first revealed that in a direction of decreasing equivalence ratios, the first transition to limit cycle state from combustion noise state was observed via intermittency. A second bifurcation was also observed, leading to quasi-period thermoacoustic instability from the limit cycle state. Intrinsic vorticity modes and natural acoustic modes could be regarded as oscillators. The competition and cooperation between the two modes led to a phenomenon beyond limit cycle states. The vortex dynamics of thermoacoustic systems are dominated by the interaction of intrinsic vorticity modes and natural acoustic modes and exhibit an adjustment of vortex shedding frequencies, resulting in different stability regions. Herein, the flame index was performed in more detail to distinguish between the premixed flame and diffusion flame. Results indicated that the burning mode was an important driver in promoting instability whilst it also served as a medium for competition and cooperation between the natural acoustic modes and intrinsic vorticity modes.

Synchronization of multiple mobile reservoir computing oscillators in complex networks

We investigate collective behavior of multiply moving reservoir computing oscillators. Each moving oscillator is fitted to a same dynamical system and then wanders a network navigating by random walk strategy. Interestingly, we find that the moving oscillators gradually present a coherent rhythmic behavior when their number is large enough. In this situation, temporal and spatial characteristics of each moving oscillator are in excellent agreement with that of their learned dynamical system under consideration. Remarkably, we show that these reservoir computing oscillators can exhibit significantly distinct collective behaviors that resemble bifurcation phenomenon when changing a critical reservoir parameter. Furthermore, we find that when studying a continuous chaotic system, intermittent synchronization emerges among these reservoir computing oscillators. But there is no evidence of enhanced correlation in the associated laminar length sequence. Our work provides a feasible framework for studying synchronization phenomena of mobile agents in nature when merely observed information is available.

Phase synchronization under mixed synapse between two heterogeneous functional neurons

Nervous system contacts and regulates the various systems and organs of the body by encoding and transmitting information, so it becomes important to explore the synaptic connections between neurons. In this study, two functional neurons are obtained by embedding Josephson junction and memristor in the FHN neuron circuit, and then based on Helmholtz’s theorem their Hamilton energies are calculated and investigated when coupled channel is awakened. There are weak but stable and orderly electromagnetic fields around human tissues and organs due to the transmembrane flow of ions, and their equilibrium state is easily disturbed and destroyed by the external electromagnetic fields, which should be considered when neuron model are investigated. Thus, an induction coil and a charge-controlled memristor (CCM) are used to perceive magnetic and electric fields respectively to couple the two function neurons, then mixed synapse is activated and synaptic plasticity is detect by parameter modulation and energy exchange. It is found that energy is continuously pumped along the coupling channel even if the synaptic connection is increased further, and two different functional neurons can only achieve quasi-phase synchronization or phase lock. However, the coupling strength threshold for achieving quasi-phase synchronization is lowered under hybrid synapses, and the possible mechanism may be that the addition of induction coil and CCM can induce time-varying electric and magnetic fields, which in turn facilitate the energy exchange in the coupled system. This study not only helps us to reveal the synchronization phenomenon of certain neurons observed in experiments, but also to explain the occurrence of pathological synchronization in the nervous system.

Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement

. The Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L 2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.

Numerical detection of synchronization phenomena in quasi‐periodic solutions

AbstractIn science and technology, dynamical systems can show so‐called quasi‐periodic solutions. These solutions are composed of two or more base frequencies. The solution in the time domain can be represented by an invariant manifold. To parametrize the invariant manifold, we choose the hyper‐time parametrization. If quasi‐periodic solutions branches are continued by means of a path continuation, the phenomenon of synchronization may occur. This is important, because the hyper‐time parametrization is only valid, as long as the number of base frequencies remains unchanged. Therefore, it is essential to detect a parametrization to a synchronization point. Synchronization can happen in different types. We address the mechanism of suppression, where one base frequency becomes suppressed until its amplitude vanishes. This corresponds to the quasi‐periodic solution ending in a Neimark–Sacker bifurcation. We present a method to derive a scalar measure from the quasi‐periodic solution in the hyper‐time parametrization, to detect an approach to a Neimark–Sacker bifurcation while continuing the solution branch.

Analytic relationship of relative synchronizability to network structure and motifs

Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of how relative synchronizability relates to underlying network structure. Indeed, this question is of central importance to the key theme of how dynamics on networks relate to their structure more generally. We present an analytic technique to directly measure the relative synchronizability of noise-driven time-series processes on networks, in terms of the directed network structure. We consider both discrete-time autoregressive processes and continuous-time Ornstein-Uhlenbeck dynamics on networks, which can represent linearizations of nonlinear systems. Our technique builds on computation of the network covariance matrix in the space orthogonal to the synchronized state, enabling it to be more general than previous work in not requiring either symmetric (undirected) or diagonalizable connectivity matrices and allowing arbitrary self-link weights. More importantly, our approach quantifies the relative synchronization specifically in terms of the contribution of process motif (walk) structures. We demonstrate that in general the relative abundance of process motifs with convergent directed walks (including feedback and feedforward loops) hinders synchronizability. We also reveal subtle differences between the motifs involved for discrete or continuous-time dynamics. Our insights analytically explain several known general results regarding synchronizability of networks, including that small-world and regular networks are less synchronizable than random networks.

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing P (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing F (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay tau _c, the average degree langle k rangle, and the rewiring probability beta have some appropriate values. When tau _c, langle k rangle, and beta are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when F increases, depending on the network topology. It is also found that the time delay tau _c can induce intermittent CS and PS whose occurrence is independent F. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.

Synchronization process expediting in nonlinear oscillators via reconfiguration of the potential well pattern

The synchronization phenomenon has garnered significant attention and extensive study due to its frequency locking effect, finding applications in diverse fields such as communication networks, neuroscience, and multi-robot systems. Fast frequency locking is crucial for synchronization applications, but there have been few investigations on it so far. In this study, we observed that when a nonlinear micro-oscillator synchronizes with a harmonic perturbation, the frequency and phase of the oscillator do not monotonically approach the locking state. Instead, they experience a period of frequency and phase fluctuations that can be divided into two stages: the slipping stage and the oscillation stage. The first slipping stage is affected by the frequency detuning between the perturbation force and oscillator, while the second oscillation stage time is determined by the configuration of the potential well. This configuration can be reconfigured by adjusting the nonlinearity terms of the micro system through phase delay, feedback strength, or perturbation strength. By reconfiguring the potential well pattern, we achieved a fivefold suppression of the synchronization process.

Investigations of complex systems’ dynamics, based on reduced amount of information: introduction to the method

Controlling dynamics of complex systems is one of the most important issues in science and engineering. Thus, there is continuous need to study and develop numerical algorithms of control methods. In this paper, we would like to present our introductory study of a new simple method of investigations of such systems based on vector field properties and reduced amount of applied information. Firstly, we present the basis of our approach for extraction of nonlinear indicators of two-dimensional systems. We show that basing on simplified analyses and exploiting half of commonly applied information, we can precisely estimate widely applied indicators. We prove that our method is simpler, more efficient and more accurate than commonly applied algorithms. After the introductory analysis, we extend our studies and apply the presented method in investigations of complex systems, based on the analysis that we discussed in the first part of the article and carried out in two-dimensional subspaces. We present simplicity and effectiveness of our approach and demonstrate how it simplifies investigations of complex dynamical phenomena. We verify our method studying the example of synchronization and chimera phenomena in the chosen set of coupled oscillators.

Quantifying the synchronization of the spikes emitted by coupled lasers

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers’ parameters. Here, we analyze experiments done with two mutually optically coupled lasers. Due to the delay in the coupling (due to the finite time the light takes to travel between the lasers), the lasers synchronize with a lag: the intensity time traces show well-defined spikes, and a spike in the intensity of one laser may occur shortly before (or shortly after) a spike in the intensity of the other laser. Measures that quantify the degree of synchronization of the lasers from the analysis of the intensity signals do not fully quantify the synchronicity of the spikes because they also take into account the synchronization of fast irregular fluctuations that occur between spikes. By analyzing only the coincidence of the spike times, we show that event synchronization measures quantify spike synchronization remarkably well. We show that these measures allow us to quantify the degree of synchronization and, also, to identify the leading laser and the lagging one.