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1.
The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent global synchronization of the networks are derived analytically. It is shown that under some conditions, if the uncoupled dynamical node is stable itself, then the network can be globally synchronized for any coupling delays as long as the coupling strength is small enough. On the other hand, if each dynamical node of the network is chaotic, then global synchronization of the networks is heavily dependent on the effects of coupling delays in addition to the connection configuration. Furthermore, the results are applied to some typical small-world (SW) and scale-free (SF) complex networks composing of coupled dynamical nodes such as the cellular neural networks (CNNs) and the chaotic FHN neuron oscillators, and numerical simulations are given to verify and also visualize the theoretical results. 相似文献
2.
M. Ponce C. C. Masoller Arturo C. Martí 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(1):83-93
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local
dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes
of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes
on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent
state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes,
focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number
of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without
a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics
that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold
connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number
of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find
that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback,
enhancing or degrading synchronization, depends on the topology and on the distribution of delays. 相似文献
3.
Robust adaptive synchronization of general dynamical networks with multiple delays and uncertainties
In this article, a general complex dynamical network which contains multiple delays and uncertainties is introduced, which contains time-varying coupling delays, time-varying node delay, and uncertainties of both the inner- and outer-coupling matrices. A robust adaptive synchronization scheme for these general complex networks with multiple delays and uncertainties is established and raised by employing the robust adaptive control principle and the Lyapunov stability theory. We choose some suitable adaptive synchronization controllers to ensure the robust synchronization of this dynamical network. The numerical simulations of the time-delay Lorenz chaotic system as local dynamical node are provided to observe and verify the viability and productivity of the theoretical research in this paper. Compared to the achievement of previous research, the research in this paper seems quite comprehensive and universal. 相似文献
4.
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach. 相似文献
5.
Fischer I Vicente R Buldú JM Peil M Mirasso CR Torrent MC García-Ojalvo J 《Physical review letters》2006,97(12):123902
We show that isochronous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of such synchronization solutions in a chain of three coupled semiconductor lasers with long interelement coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that zero-lag synchronized chaotic dynamical states can occur over long distances through relaying, without restriction by the amount of delay. 相似文献
6.
Synchronization of time-delay chaotic systems on small-world networks with delayed coupling 下载免费PDF全文
By using the well-known Ikeda model as the node dynamics, this paper
studies synchronization of time-delay systems on small-world
networks where the connections between units involve time delays. It
shows that, in contrast with the undelayed case, networks with
delays can actually synchronize more easily. Specifically, for
randomly distributed delays, time-delayed mutual coupling suppresses
the chaotic behaviour by stabilizing a fixed point that is unstable
for the uncoupled dynamical system. 相似文献
7.
Global synchronization of Chua's chaotic delay network by using linear matrix inequality 总被引:3,自引:0,他引:3 下载免费PDF全文
Global synchronization of Chua‘s chaotic dynamical networks with coupling delays is investigated in this paper.Unlike other approaches, where only local results were obtained, the network is found to be not linearized in this paper.Insteat, the global synchronization is obtained by using the linear matrix inequality theory. Moreover, some quite simple linear-state-error feedback controllers for global synchronization are derived, which can be easily constructed based on the minimum eigenvalue of the coupling matrix. A simulation of Chua‘s chaotic network with global coupling delays in nodes is finally given, which is used to verify the theoretical results of the proposed global synchron izationscheme. 相似文献
8.
The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations. 相似文献
9.
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network
topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the
elements of the network are identical (N logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling
strengths are uniform throughout the network. We show that if the delay times are sufficiently heterogeneous, for adequate
coupling strength the network synchronizes in a spatially homogeneous steady state, which is unstable for the individual maps
without coupling. This synchronization behavior is referred to as ‘suppression of chaos by random delays’ and is in contrast
with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network
synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence
of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central
node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently
heterogeneous the synchronization behavior is largely independent of the network topology but depends on the network’s connectivity,
i.e., on the average number of neighbors per node.
相似文献
10.
11.
Two different kinds of synchronization have been applied to cryptography: synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the external signal to the chaotic maps is synchronized by the nets, we construct a hybrid network which allows a secure generation of secret encryption keys over a public channel. The security with respect to attacks, recently proposed by Shamir et al., is increased by chaotic synchronization. 相似文献
12.
Complete and phase synchronization in a heterogeneous small-world neuronal network 总被引:1,自引:0,他引:1 下载免费PDF全文
Synchronous firing of neurons is thought to be important for
information communication in neuronal networks. This paper
investigates the complete and phase synchronization in a
heterogeneous small-world chaotic Hindmarsh--Rose neuronal network.
The effects of various network parameters on synchronization
behaviour are discussed with some biological explanations. Complete
synchronization of small-world neuronal networks is studied
theoretically by the master stability function method. It is shown
that the coupling strength necessary for complete or phase
synchronization decreases with the neuron number, the node degree
and the connection density are increased. The effect of
heterogeneity of neuronal networks is also considered and it is
found that the network heterogeneity has an adverse effect on
synchrony. 相似文献
13.
C. Masoller F.M. Atay 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,62(1):119-126
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. 相似文献
14.
This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays.Within the new framework,closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way,where the feedback matrix is determined through consideration of the coordination of the node dynamics,the inner connected matrix and the outer connected matrix.Unlike previously existing results,the feedback gain matrix here is decoupled from the inner matrix;this not only guarantees the flexible choice of the gain matrix,but also leaves much space for inner matrix configuration.Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction,which works in a distributed way between individual neighbours,and the linear feedback control for each node.Provided that the network is connected and balanced,synchronization will come true naturally,where theoretical proof is given via a Lyapunov function.For completeness,several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme. 相似文献
15.
We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have equal input and output weight sums. We obtain the same upper bound for synchronization in asymmetrically connected networks as in the network with a symmetrized matrix, provided that the condition of node balance is satisfied. In terms of graphs, the symmetrization operation amounts to replacing each directed edge by an undirected edge of half the coupling strength. It should be stressed that without node balance this property in general does not hold. 相似文献
16.
This paper introduces the concept of linear-control-based
synchronization of coexisting attractor networks with time delays.
Within the new framework, closed loop control for each dynamic node
is realized through linear state feedback around its own arena in a
decentralized way, where the feedback matrix is determined through
consideration of the coordination of the node dynamics, the
inner connected matrix and the outer connected matrix. Unlike
previously existing results, the feedback gain matrix here is decoupled
from the inner matrix; this not only guarantees the flexible choice
of the gain matrix, but also leaves much space for inner matrix
configuration. Synchronization of coexisting attractor networks with
time delays is made possible in virtue of local interaction, which
works in a distributed way between individual neighbours, and the
linear feedback control for each node. Provided that the network is
connected and balanced, synchronization will come true naturally,
where theoretical proof is given via a Lyapunov function. For
completeness, several illustrative examples are presented to further
elucidate the novelty and efficacy of the proposed scheme. 相似文献
17.
We study synchronization transitions and pattern formation on small-world networks consisting of Morris-Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity. 相似文献
18.
We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles. 相似文献
19.
《Chinese Journal of Physics (Taipei)》2018,56(4):1488-1496
A new piecewise linear unified chaotic (PLUC) system is firstly presented, and then its fundamental dynamical behaviors are analyzed. This modified chaotic system, as well as the unified chaotic (UC) one, is taken as network nodal oscillators for investigating the difference of influences of nodal dynamics on the bifurcation of network synchronized regions. It is found that beyond the greatly similar bifurcation modes between PLUC and UC networks, the synchronized regions in PLUC networks are far narrower at almost each parameter a than those in UC networks for most of inner coupling matrices, indicating the PLUC node makes the network more difficult to synchronization. Our numerical investigations show that this phenomenon is closely related with nodal dynamical properties, such as the boundary of attractors, the largest Lyapunov exponent and Lyapunov dimension. 相似文献
20.
O. Moskalenko N. Phrolov A. Koronovskii A. Hramov 《The European physical journal. Special topics》2013,222(10):2571-2582
Time scale synchronization in networks of chaotic microwave oscillators with the different topologies of the links between nodes has been studied. As a node element of the network the one-dimensional distributed model of the low-voltage vircator has been used. To characterize the degree of synchronization in the whole network the synchronization index has been introduced. The transition to the synchronous regime is shown to take place via cluster time scale synchronization. Meanwhile, the spectral structure of the output signals is complicated sufficiently which allows using such devices in a number of practical applications. 相似文献