Unsynchronized State Research Articles

Changes in cross-boundary coalescence effects induce the unsynchronized states shift of microbial structure and microbial-mediated nitrogen-cycle pathways in coupled-ecosystem

Understanding the coalescence of materials and microorganisms across pre-configured functional zones in coupled ecosystems is crucial for refining ecological restoration strategies. Deciphering how this coalescence triggers changes in state and functionality is key. However, the emergence of alternative states due to coalescence impacts could lead to abrupt ecological changes near boundaries, with unknown implications. This study focused on a typical coupled ecosystem, constructed wetland (CW), to investigate the impact of coalescence on shifts in aquatic microbial community states. A quantitative method and hierarchical linear models with Bayesian inference were used. Results showed a gradual increase in coalescence from inlet to outlet, with upstream points significantly influencing downstream points (54.13%, 62.35%, 84.03% for each pond). Alternative stable states were found in microbial-mediated nitrogen cycle pathways, leading to a transition from robust denitrification to diminished ammonification and denitrification states. This shift correlated strongly with community cohesion and nitrogen concentration. The observed change in state shift lagged 5% of the total CW length compared to the change in functional states. This research highlights the potential for targeted manipulation of microbial assemblages in CWs for ecological management and restoration.

Intermittent chimera-like and bi-stable synchronization states in network of distinct Izhikevich neurons

Phase synchronization phenomena of neuronal networks are one of many features depicted by real networks that can be studied using computational models. Here, we proceed with numerical simulations of a globally connected network composed of non-identical (distinct) Izhikevich neuron model to study clustered phase synchronization. We investigate the case in which, once coupled, there exist two main neuron clusters in the network: one of them is bi-stable, depicting phase-synchronized or unsynchronized states, depending on the initial conditions; and the second one shows just an unsynchronized state. For the set of initial conditions that lead the first cluster to the synchronized regime, we observe a chimera-like pattern of the network. For small networks, the dynamics can also present intermittent chimera-like scenarios. In this context, the mechanism for intermittent chimera states is based on two features: the coexistence of a synchronized cluster with an unsynchronized one; and the capability of one cluster to display bi-stability depending on the signal trait by which it is forced. We conclude with an understanding of intermittent chimera-like dynamics as the limit case where bi-stability is not maintained, which occurs due to the loss of uniformity in the neuron input synaptic currents.

Dynamic behaviors in two-layer coupled oscillator system

In this paper, we present a two-layer coupled oscillator model, in which the first layer is composed of the nearest neighbor coupled identical oscillator, the second layer is composed of the global coupled identical oscillator, and there is a one-way point-to-point drive from the second layer to the first layer. In this system, the driven layer changes from unsynchronized state to synchronized state with the change of parameters. During this transformation, we found the existence of chimer state. And the dynamic behavior of the system had been studied. The critical value for the state transition had been caught.

Numerical study of superradiant mixing by an unsynchronized superradiant state of multiple atomic ensembles

We numerically analyze superradiant dynamics in atomic ensembles that have different transition frequencies using a numerical model that can take account of the transient behavior of an unsynchronized superradiant state. The numerical results unveil that the superradiant emission of a periodic pulse train can be induced by means of collective multiple frequency generation, which we call superradiant mixing. This is, in fact, due to the superradiant coupling of unsynchronized atomic ensembles. We numerically investigate the superradiant mixing in detail, varying the collective decay rate, repumping rate, and the number of the individual atomic ensembles with detuned frequencies. This work broadens our understanding of the collective atomic behavior in a detuned system, and it also suggests a novel method for frequency generation without relying on the conventional Kerr nonlinear effect.

A Brief Review of Chimera State in Empirical Brain Networks.

Understanding the human brain and its functions has always been an interesting and challenging problem. Recently, a significant progress on this problem has been achieved on the aspect of chimera state where a coexistence of synchronized and unsynchronized states can be sustained in identical oscillators. This counterintuitive phenomenon is closely related to the unihemispheric sleep in some marine mammals and birds and has recently gotten a hot attention in neural systems, except the previous studies in non-neural systems such as phase oscillators. This review will briefly summarize the main results of chimera state in neuronal systems and pay special attention to the network of cerebral cortex, aiming to accelerate the study of chimera state in brain networks. Some outlooks are also discussed.

Chimera states in hybrid coupled neuron populations

Here we study the emergence of chimera states, a recently reported phenomenon referring to the coexistence of synchronized and unsynchronized dynamical units, in a population of Morris–Lecar neurons which are coupled by both electrical and chemical synapses, constituting a hybrid synaptic architecture, as in actual brain connectivity. This scheme consists of a nonlocal network where the nearest neighbor neurons are coupled by electrical synapses, while the synapses from more distant neurons are of the chemical type. We demonstrate that peculiar dynamical behaviors, including chimera state and traveling wave, exist in such a hybrid coupled neural system, and analyze how the relative abundance of chemical and electrical synapses affects the features of chimera and different synchrony states (i.e. incoherent, traveling wave and coherent) and the regions in the space of relevant parameters for their emergence. Additionally, we show that, when the relative population of chemical synapses increases further, a new intriguing chaotic dynamical behavior appears above the region for chimera states. This is characterized by the coexistence of two distinct synchronized states with different amplitude, and an unsynchronized state, that we denote as a chaotic amplitude chimera. We also discuss about the computational implications of such state.

Protocol for suppression of phase synchronization in Hodgkin–Huxley-type networks

Phase synchronization of neurons is fundamental for the functioning of the human brain which can be related to neurological diseases such as Parkinson and/or seizure behaviors generated by epilepsy. For small-world networks, an atypically high level of phase synchronization may occur even for unexpected low values of the coupling strength when compared to traditional critical values which delimit the transition from a globally stable unsynchronized to a globally stable phase synchronized states. This regime is characterized by a non-monotonic transition as a function of the coupling parameter. In order to study this phenomenon, we consider a neural network composed of 5,000 Hodgkin–Huxley-type neurons, coupled by a small-world connection matrix. Based on suppression protocols of phase synchronization, we study how this abnormal phase synchronization can be suppressed by applying an external pulsed current in the network. It is shown that the synchronization for weak coupling can be suppressed without any visible effect in the globally stable asymptotic state occurring for higher values of the coupling strength. We also demonstrate that to preserve the unsynchronized state, the external current must be kept switched on, otherwise, the abnormal synchronization regime is recovered due to the globally stable state present on the dynamics. Optimization protocols are studied by varying the amplitude and time intervals of the current pulses.

Generalized synchronization in a conservative and nearly conservative systems of star network.

We report the coexistence of synchronized and unsynchronized states in a mutually coupled star network of nearly conservative non-identical oscillators. Generalized synchronization is observed between the central oscillator with the peripherals, and phase synchronization is found among the peripherals in weakly dissipative systems. However, the basin size of the synchronization region decreases as dissipation strength is increased. We have demonstrated these phenomena with the help of Duffing and Lorenz84 oscillators with conservative, nearly conservative, and dissipative properties. The observed results are robust against the network size.

Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators.

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter (here for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, , aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime.

Multistability and variations in basin of attraction in power-grid systems

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes’ recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the unsynchronized states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

An Analytical Study on the Synchronization of Murali—Lakshmanan—Chua Circuits

An explicit analytical solution is presented for unidirectionally coupled two Murali—Lakshmanan—Chua circuits exhibiting chaos synchronization in their dynamics. The transition of the system from an unsynchronized state to a state of complete synchronization under the influence of the coupling parameter is observed through phase portraits obtained from the analytical solutions of the circuit equations characterizing the system.

Kuramoto-type phase transition with metronomes

Metronomes placed on the perimeter of a disc-shaped platform, which can freely rotate in a horizontal plane, are used for a simple classroom illustration of the Kuramoto-type phase transition. The rotating platform induces a global coupling between the metronomes, and the strength of this coupling can be varied by tilting the metronomes’ swinging plane relative to the radial direction on the disc. As a function of the tilting angle, a transition from spontaneously synchronized to unsynchronized states is observable. By varying the number of metronomes on the disc, finite-size effects are also exemplified. A realistic theoretical model is introduced and used to reproduce the observed results. Computer simulations of this model allow a detailed investigation of the emerging collective behaviour in this system.

Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

Sparsely-synchronized brain rhythm in a small-world neural network

Sparsely-synchronized cortical rhythms, associated with diverse cognitive functions, have been observed in electric recordings of brain activity. At the population level, cortical rhythms exhibit small-amplitude fast oscillations while at the cellular level, individual neurons show stochastic firings sparsely at a much lower rate than the population rate. We study the effect of network architecture on sparse synchronization in an inhibitory population of subthreshold Morris-Lecar neurons (which cannot fire spontaneously without noise). Previously, sparse synchronization was found to occur for cases of both global coupling (i.e., regular all-to-all coupling) and random coupling. However, a real neural network is known to be non-regular and non-random. Here, we consider sparse Watts-Strogatz small-world networks which interpolate between a regular lattice and a random graph via rewiring. We start from a regular lattice with only short-range connections and then investigate the emergence of sparse synchronization by increasing the rewiring probability p for the short-range connections. For p = 0, the average synaptic path length between pairs of neurons becomes long; hence, only an unsynchronized population state exists because the global efficiency of information transfer is low. However, as p is increased, long-range connections begin to appear, and global effective communication between distant neurons may be available via shorter synaptic paths. Consequently, as p passes a threshold p th (}~ 0.044), sparsely-synchronized population rhythms emerge. However, with increasing p, longer axon wirings become expensive because of their material and energy costs. At an optimal value p* DE (}~ 0.24) of the rewiring probability, the ratio of the synchrony degree to the wiring cost is found to become maximal. In this way, an optimal sparse synchronization is found to occur at a minimal wiring cost in an economic small-world network through trade-off between synchrony and wiring cost.

One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes

We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent α of the power law is taken in the range 0≤α<1. The oscillator frequency distribution is symmetric about its mean (taken to be zero) and is nonincreasing on [0,∞). In the continuum limit, the local density of oscillators evolves in time following the continuity equation that expresses the conservation of the number of oscillators of each frequency under the dynamics. This equation admits as a stationary solution the unsynchronized state uniform both in phase and over the space of the lattice. We perform a linear stability analysis of this state to show that when it is unstable, different spatial Fourier modes of fluctuations have different stability thresholds beyond which they grow exponentially in time with rates that depend on the Fourier modes. However, numerical simulations show that at long times all the nonzero Fourier modes decay in time, while only the zero Fourier mode (i.e., the "mean-field" mode) grows in time, thereby dominating the instability process and driving the system to a synchronized state. Our theoretical analysis is supported by extensive numerical simulations.

Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [F.M. Atay, J. Jost, A. Wende, Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [C. Masoller, A.C. Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes.

Synchronization of oscillators with long-range power law interactions

We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent α(c) across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find α(c)=3/2. Frequency entrainment and phase ordering are discussed as a function of α≥1 . The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the d -dimensional problem.

Symbolic synchronization and the detection of global properties of coupled dynamics from local information

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.

Long-time anticipation of chaotic states in time-delay coupled ring and linear arrays

We study the time-delay and unidirectionally coupled ring and linear arrays of chaotic systems, and find that under certain conditions, the linear array can spatial periodically "copy" the chaotic dynamics of the ring with very long anticipation times. Numerical calculations of the Lyapunov exponents show that the delay times can result in unsynchronized chaotic waves, periodic waves, and stable states in the ring that are replicated in the linear array, but have no effect on the absolute stability of the anticipatory synchronization. Our results show that such configurations can both enhance the absolute stability of the synchronization manifolds and minimize the effects of convective instabilities.

Multiuser detection with decorrelating detector for asynchronous CDMA systems

AbstractMultiuser detection using decorrelating detectors in CDMA systems have favorable performance when a few channels are in the synchronized state. However, when there are many channels, the performance degrades due to the effect of intersymbol interference in the unsynchronized state and the effect of noise emphasis. In this paper, we propose a method that reduces the effects between adjacent symbols by adding a guard chip interval while not increasing the processing computational load of the decorrelating detector even in the unsynchronized state. In addition, we propose a method that applies quasi‐maximum likelihood estimation, a simplification of maximum likelihood estimation, to reduce the degradation in the noise emphasis. The result of an evaluation of the BER performance by a computer simulation verified the removal of interference nearly equal to the synchronized state even in the unsynchronized state. Even if the performance is degraded by the effect of noise emphasis with many channels, we verified that the performance can be improved to some degree by applying quasi‐maximum likelihood estimation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(1): 32–43, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20139