共查询到20条相似文献,搜索用时 21 毫秒
1.
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled Hindmarsh-Rose and Morris-Lecar oscillators. Finally we discuss possible “instabilities” in networks of oscillators induced by the diffusive coupling. 相似文献
2.
We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system. 相似文献
3.
P. M. Gleiser D. H. Zanette 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(2):233-238
We analyze the interplay of synchronization and structure
evolution in an evolving network of phase oscillators. An initially
random network is adaptively rewired according to the dynamical
coherence of the oscillators, in order to enhance their mutual
synchronization. We show that the evolving network reaches a
small-world structure. Its clustering coefficient attains a maximum
for an intermediate intensity of the coupling between oscillators,
where a rich diversity of synchronized oscillator groups is
observed. In the stationary state, these synchronized groups are
directly associated with network clusters. 相似文献
4.
Fumito Mori 《Physica D: Nonlinear Phenomena》2009,238(14):1180-1185
We investigate the synchronous dynamics of Kuramoto oscillators and van der Pol oscillators on Watts-Strogatz type small-world networks. The order parameters to characterize macroscopic synchronization are calculated by numerical integration. We focus on the difference between frequency synchronization and phase synchronization. In both oscillator systems, the critical coupling strength of the phase order is larger than that of the frequency order for the small-world networks. The critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one. For the Kuramoto oscillators, the behavior can be described by a power-law function and the exponents are obtained for the two synchronizations. The separation of the critical point between the phase and frequency synchronizations is found only for small-world networks in the theoretical models studied. 相似文献
5.
Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back. 相似文献
6.
Guy Katriel 《Physica D: Nonlinear Phenomena》2008,237(22):2933-2944
We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ-ω oscillators. 相似文献
7.
Global synchronization in arrays of coupled networks with one single time-varying delay coupling is investigated in this Letter. A general linear coupled network with a time-varying coupling delay is proposed and its global synchronization is further discussed. Some sufficient criteria are derived based on Lyapunov functional and linear matrix inequality (LMI). It is shown that under one single delay coupling, the synchronized state changes, which is different from the conventional synchronized solution. Moreover, the degree of the nodes and the inner delayed coupling matrix play key roles in the synchronized state. In particular, the derivative of the time-varying delay can be any given value. Finally, numerical simulations are given to illustrate the theoretical results. 相似文献
8.
D.H. Zanette 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(3):537-541
A system of globally coupled maps whose synchronized dynamics differs from the individual (chaotic) evolution is considered.
For nonchaotic synchronized dynamics, the synchronized state becomes stable at a critical coupling intensity lower than that
of the fully chaotic case. Below such critical point, synchronization is also stable in a set of finite intervals. Moreover,
the system is shown to exhibit multistability, so that even when the synchronized state is stable not all the initial conditions
lead to synchronization of the ensemble.
Received 22 October 1999 相似文献
9.
Synchronized Anti-Phase and In-Phase Oscillations of Intracellular Calcium Ions in Two Coupled Hepatocytes System 下载免费PDF全文
We study the dynamic behaviour of two intracellufar calcium oscillators that are coupled through gap junctions both to Ca^2+ and inositol(1,4,5)-trisphosphate (IP3). It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic cadcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca^2+ and IP3 among cells on synchronous behaviour, are considered. We fnd that small coupling of Ca^2+ and large coupling of IP3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling. 相似文献
10.
M. N. Kuperman D. H. Zanette 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(2):243-248
Inspired by Axelrod’s model of culture dissemination, we
introduce and analyze a model for a population of coupled
oscillators where different levels of synchronization can be
assimilated to different degrees of cultural organization. The
state of each oscillator is represented by a set of phases, and
the interaction – which occurs between homologous phases – is
weighted by a decreasing function of the distance between
individual states. Both ordered arrays and random networks are
considered. We find that the transition between synchronization
and incoherent behaviour is mediated by a clustering regime with
rich organizational structure, where any two oscillators can be
synchronized in some of their phases, while their remain
unsynchronized in the others. 相似文献
11.
Isao Nishikawa Naofumi Tsukamoto Kazuyuki Aihara 《Physica D: Nonlinear Phenomena》2009,238(14):1197-1202
We investigate chaotic phase synchronization (CPS) in three-coupled chaotic oscillator systems. According to the coupling strength and mismatches in the frequencies of these oscillators, we can observe complete CPS where all three oscillators exhibit CPS, and partial CPS where only two oscillators exhibit CPS. When the coupling strength is weakened, we observe a phenomenon that complete CPS among the three oscillators is suddenly disrupted without going through partial CPS. In this case oscillators exhibit quasi-CPS where two oscillators appear to exhibit CPS transiently, and the combination of the two oscillators changes with time. We call this phenomenon CPS switching D. It is revealed that phase fluctuation plays an important role in CPS switching D. It is also shown that the amplitude with a specific structure strengthens the degree of CPS switching. In the present paper, we characterize this CPS switching and discuss its mechanism. 相似文献
12.
N. Kouvaris A. Provata 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(4):535-541
Long distance reactive and diffusive coupling is introduced in a spatially extended nonlinear stochastic network of interacting
particles. The network serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. If the network includes
only local nearest neighbour interactions, the system organizes into a number of local asynchronous oscillators. It is shown
that (a) Introduction of all-to-all coupling in the network leads the system into global, center-type, conservative oscillations
as dictated by the mean-field dynamics. (b) Introduction of reactive coupling to the network leads the system to intermittent
oscillations where the trajectories stick for short times in bounded regions of space, with subsequent jumps between different
bounded regions. (c) Introduction of diffusive coupling to the system does not alter the dynamics for small values of the
diffusive coupling pdiff, while after a critical value pdiff
c the system synchronizes into a limit cycle with specific frequency, deviating non-trivially from the mean-field center-type
behaviour. The frequency of the limit cycle oscillations depends on the reaction rates and on the diffusion coupling. The
amplitude σ of the limit cycle depends on the control parameter pdiff. 相似文献
13.
Gabriel H. Paissan 《Physica D: Nonlinear Phenomena》2008,237(6):818-828
We consider an extension of Kuramoto’s model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an oscillator, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each oscillator to the mean field, and the coupling of each oscillator to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where oscillators become entrained in synchronized frequency clusters. 相似文献
14.
We compare two methods for detecting phase synchronization in coupled non-phase-coherent oscillators. One method is based on the locking of self-sustained oscillators with an irregular signal. The other uses trajectory recurrences in phase space. We identify the pros and cons of both methods and propose guidelines to detect phase synchronization in data series. 相似文献
15.
We study the synchronization of coupled phase oscillators in random complex networks. The topology of the networks is assumed to be vary over time. Here we mainly study the onset of global phase synchronization when the topology switches rapidly over time. We find that the results are, to some extent, different from those in deterministic situations. In particular, the synchronizability of coupled oscillators can be enhanced in ER networks and scale-free networks under fast switching, while in stochastic small-world networks such enhancement is not significant. 相似文献
16.
Wei Yang 《Physics letters. A》2010,374(4):557-3089
In this Letter, we investigate function projective synchronization of two-cell quantum-CNN chaotic oscillators using nonlinear adaptive controller. Based on Lyapunov stability theory, the nonlinear adaptive control law is derived to make the state of two chaotic systems function projective synchronized. Two numerical simulations are presented to illustrate the effectiveness of the proposed nonlinear adaptive control scheme, which is more effective than that in previous literature. 相似文献
17.
The behaviors of coupled oscillators, each of which has periodic
motion with random natural frequency in the absence of coupling, are
investigated when phase shifts are considered. In the system of
coupled oscillators, phase shifts are the same between different
oscillators. Synchronization and synchronization transition are
revealed with different phase shifts. Phase shifts play an important
role for this kind of system. When the phase shift α<0.5π,
the synchronization state can be attained by increasing the
coupling, and the system cannot reach the synchronization state
while α≥q0.5π. A clear scaling between complete
synchronization critical coupling strength K_pc and
α-0.5π is found. 相似文献
18.
Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay 下载免费PDF全文
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. 相似文献
19.
《理论物理通讯》2015,(12)
For an oscillating circuit or coupled circuits,damage in electric devices such as inductor,resistance,memristor even capacitor can cause breakdown or collapse of the circuits. These damage could be associated with external attack or aging in electric devices,and then the bifurcation parameters could be deformed from normal values. Resonators or signal generators are often synchronized to produce powerful signal series and this problem could be investigated by using synchronization in network. Complete synchronization could be induced by linear coupling in a two-dimensional network of identical oscillators when the coupling intensity is beyond certain threshold. The collective behavior and synchronization state are much dependent on the bifurcation parameters. Any slight fluctuation in parameter and breakdown in bifurcation parameter can cause transition of synchronization even collapse of synchronization in the network. In this paper,a two-dimensional network composed of the resonators coupled with memristors under nearestneighbor connection is designed,and the network can reach complete synchronization by carefully selecting coupling intensity. The network keeps synchronization after certain transient period,then a bifurcation parameter in a resonator is switched from the previous value and the adjacent resonators(oscillators) are affected in random. It is found that the synchronization area could be invaded greatly in a diffusive way. The damage area size is much dependent on the selection of diffusive period of damage and deformation degree in the parameter. Indeed,the synchronization area could keep intact at largest size under intermediate deformation degree and coupling intensity. 相似文献
20.
Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling 下载免费PDF全文
In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays. 相似文献