Random shortcuts induce phase synchronization in complex Chua systems

This paper studies how phase synchronization in complex networks depends on random shortcuts, using the piecewise-continuous chaotic Chua system as the nodes of the networks. It is found that for a given coupling strength, when the number of random shortcuts is greater than a threshold the phase synchronization is induced. Phase synchronization becomes evident and reaches its maximum as the number of random shortcuts is further increased. These phenomena imply that random shortcuts can induce and enhance the phase synchronization in complex Chua systems. Furthermore, the paper also investigates the effects of the coupling strength and it is found that stronger coupling makes it easier to obtain the complete phase synchronization.     

Synchronization of Modified Chua＇s Circuit with x｜x｜ Function

This paper considers the chaos synchronization of the modified Chua＇s circuit with x｜x｜ function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach.     

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.     

Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators

We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models.     

Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization

In this paper, we perform theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. The Chua chaotic system is applied as the original system, and its time series of a single variable is applied as a feedback variable to drive a simulative system. The simplex method is employed to minimize the synchronization error in the simulative system to iteratively approach the original system parameters. Furthermore, the effects of feedback function, feedback weight, and noise are investigated. The parameter estimation method based on feedback synchronization shows its robustness to noise perturbation. Finally, the circuit experiment of parameter estimation is implemented in order to examine its practical applicability. The original Chua circuit parameters can be well approached from its recorded time series of a single variable. The results show the parameter estimation method based on feedback synchronization may be capable of estimating real system parameters from a chaotic time series.     

Crowd synchrony and quorum sensing in delay-coupled lasers

Crowd synchrony and quorum sensing arise when a large number of dynamical elements communicate with each other via a common information pool. Previous evidence has shown that this type of coupling leads to synchronization, when coupling is instantaneous and the number of coupled elements is large enough. Here we consider a situation in which the transmission of information between the system components and the coupling pool is not instantaneous. To that end, we model a system of semiconductor lasers optically coupled to a central laser with a delay. Our results show that, even though the lasers are nonidentical due to their distinct optical frequencies, zero-lag synchronization arises. By changing a system parameter, we can switch between two different types of synchronization transition. The dependence of the transition with respect to the delay-coupling parameters is studied.     

Characteristics and synchronization of time-delay systems driven by a common noise

We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them.     

Enhancement of neural synchrony by time delay

In a network of neuronal oscillators with time-delayed coupling, we uncover a phenomenon of enhancement of neural synchrony by time delay: a stable synchronized state exists at low coupling strengths for significant time delays. By formulating a master stability equation for time-delayed networks of Hindmarsh-Rose neurons, we show that there is always an extended region of stable synchronous activity corresponding to low coupling strengths. Such synchrony could be achieved in the undelayed system only by much higher coupling strengths. This phenomenon of enhanced neural synchrony by delay has important implications, in particular, in understanding synchronization of distant neurons and information processing in the brain.     

Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay

Average synchronization and temporal order characterized by the rate of firing are studied in a spatially extended network system with the coupling time delay, which is locally modelled by a two-dimensional Rulkov map neuron. It is shown that there exists an optimal noise level, where average synchronization and temporal order are maximum irrespective of the coupling time delay. Furthermore, it is found that temporal order is weakened when the coupling time delay appears. However, the coupling time delay has a twofold effect on average synchronization, one associated with its increase, the other with its decrease. This clearly manifests that random perturbations and time delay play a complementary role in synchronization and temporal order.     

“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步

以修正过的Morris-Lecar神经元模型为例,讨论了“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步行为.首先,分别考察了同一拓扑类型的两个耦合簇放电神经元的同步行为,发现“Hopf/homoclinic”簇放电比“SubHopf/homoclinic”簇放电达到膜电位完全同步所需要的耦合强度小,即前者比后者更容易达到膜电位完全同步.其次,对这两个不同拓扑类型的簇放电神经元的耦合同步行为进行了讨论.通过数值分析发现随着耦合强度的增加,两种不同类型的簇放电首先达到簇放电同步,然后当耦合强度足够大时甚至可以达到膜电位完全同步,并且同步后的放电类型更接近容易同步的簇放电类型,即“Hopf/homoclinic”簇放电.然而令人奇怪的是此时慢变量并没有达到完全同步,而是相位同步;慢变量之间呈现为一种线性关系.这一点和现有文献的结果截然不同.     

Dual-lag synchronization between coupled chaotic lasers due to path-delay interference

We study experimentally the synchronization dynamics of two semiconductor lasers coupled unidirectionally via two different delayed paths. The emitter laser operates in a chaotic regime characterized by low-frequency fluctuations due to optical feedback and induces a synchronized dynamical activity in the receiver laser, which operates in the continuous-wave regime when uncoupled. Different delays in the two coupling paths lead to the coexistence of two time lags in the synchronized dynamics of the oscillators. This dual-lag synchronization degrades the average synchronization quality of the system of coupled lasers and hinders the transmission of information between them. Numerical simulation results agree with the experimental observations, and allow us to explore this phenomenon in a wide parameter range, and quantify the degree of signal transmission degradation caused by this chaotic path-delay interference.     

Implications of heterogeneous inputs and connectivity on the synchronization in excitable networks

We study the combined implications of connectivity and heterogeneous inputs on the synchronization features of a one-dimensional chain of diffusively coupled FitzHugh Nagumo (FHN) systems. The uncoupled systems are triggered into a regime of chaotic firing by periodic parametric forces modeling external stimuli. Due to the parameter dispersion involved in randomly distributed amplitudes and/or phases of the forces the units are nonidentical and the firing events on the chain of uncoupled units will be asynchronous leading to a distribution of the spiking times. Interest is focused on mutually synchronized spikings arising through the coupling where the connectivity of the network may range from nearest-neighbor interaction to global interactions. From our studies we conclude that increasing the interaction radius does not necessarily entail better spike synchrony and the coupling strength plays a more important role than connectivity. It is found that for driving with random amplitudes together with random phases a critical interaction radius exists beyond which firing becomes suppressed if the coupling between the units is too strong. In such cases of ‘firing death’ the units perform only small-amplitude oscillations which are mutually synchronous. The optimal coupling for spike synchrony is of intermediate strength and altering the connectivity does not really matter for the degree of spike synchrony. Distinct to that, when all the phases are equal and only the amplitudes of the forces are randomly distributed enhanced spike synchrony is achieved for sufficiently strong coupling regardless of the interaction radius.     

On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators

We study synchrony optimized networks. In particular, we focus on the Kuramoto model with non-identical native frequencies on a random graph. In a first step, we generate synchrony optimized networks using a dynamic breeding algorithm, whereby an initial network is successively rewired toward increased synchronization. These networks are characterized by a large anti-correlation between neighbouring frequencies. In a second step, the central part of our paper, we show that synchrony optimized networks can be generated much more cost efficiently by minimization of an energy-like quantity E and subsequent random rewires to control the average path length. We demonstrate that synchrony optimized networks are characterized by a balance between two opposing structural properties: A large number of links between positive and negative frequencies of equal magnitude and a small average path length. Remarkably, these networks show the same synchronization behaviour as those networks generated by the dynamic rewiring process. Interestingly, synchrony-optimized network also exhibit significantly enhanced synchronization behaviour for weak coupling, below the onset of global synchronization, with linear growth of the order parameter with increasing coupling strength. We identify the underlying dynamical and topological structures, which give rise to this atypical local synchronization, and provide a simple analytical argument for its explanation.     

The effect of distributed time-delays on the synchronization of neuronal networks

Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the distributed delays. We also notice that a normal distribution of delays gives rise to a transition at marginally lower coupling strengths, vis-a-vis uniformly distributed delays. These trends hold across classes of networks and for varying standard deviations of the delay distribution, indicating the generality of these results. So we conclude that distributed delays, which may be typically expected in real-world situations, do not have a notable effect on synchronization. This allows results obtained with constant delays to remain relevant even in the case of randomly distributed delays.     

Quantum stochastic synchronization

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength alpha > 1) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes.     

Parameter estimation using balanced synchronization

Synchronization between experimental observations and a dynamical model with undetermined parameters can assist in completing the specification of the model parameters. The quality of the synchronization, a cost function to be minimized, typically depends on the difference between the data time series and the model time series. If the coupling between the data and the model is too strong, this cost function is small for any data and any model, and the variation of the cost function with respect to the parameters of interest is too small to permit selection of a value of the parameters. If the coupling is too small, synchronization is lost. We introduce two methods for balancing the competing desires of a small cost function and the numerical ability to determine parameters accurately. One method of ‘balanced’ synchronization adds a requirement that the conditional Lyapunov exponent of the model system, conditioned on being driven by the data, remain negative but small. The other method allows the coupling to vary in time according to the error in synchronization. This second method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined.     

混沌同步的充分条件及应用

对两大类常用连续混沌系统，给出了同步的充分条件，以及状态变量的演化范围，对其作了证明，从理论上分析了这些充分条件一定可实现. 作为应用，证明了时变参数混沌同步的实现充分条件，并用Chua系统仿真实现. 时变参数混沌同步通信具有强抗破译性，也给出其抗破译的仿真. 关键词： 条件Lyapunov指数(CLE) Chua电路 参数同步     

Adaptive synchronization of memristor-based Chuaʼs circuits

In this Letter, a memristor-based Chua?s system is presented, and the chaotic behavior of this system is demonstrated by phase portraits. This Letter also deals with the problem of adaptive synchronization control of this chaotic system using the drive–response concept, and presents an adaptive control scheme for the synchronization of memristor-based Chua?s circuit, when the parameters of the drive system are fully unknown and different with those of the response system. The sufficient condition for the adaptive synchronization has been analyzed. Moreover, the controller design method is further extended to more general cases, where the physical plant contains parameter uncertainties, represented in either polytopic or structured frameworks. Numerical simulations are used to demonstrate these results.     

Synchronization of bursting neurons: what matters in the network topology

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.     

Hindmarsh-Rose神经元的随机自共振和噪声影响下的同步

研究了噪声对Hindmarsh-Rose(HR)神经元随机自共振和同步的影响。将高斯白噪声加入HR神经元模型的膜电位上，把外界直流电作为分岔参数，分别考虑参数处于Hopf分岔前、Hopf分岔附近和Hopf分岔后时，噪声影响下的随机自共振现象。两个未经耦合的全同HR神经元，如果接受相同的噪声激励，只要噪声强度高于某临界值，就能达到完全同步。进一步，噪声能够增强弱耦合神经元的完全同步。数值结果表明簇放电的神经元比峰放电的神经元更容易被噪声诱导而达到完全同步，耦合也增强了神经元对噪声激励的灵敏度。