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1.
Arkady Pikovsky 《Physica D: Nonlinear Phenomena》2009,238(1):27-37
We analyze a minimal model of a population of identical oscillators with a nonlinear coupling—a generalization of the popular Kuramoto model. In addition to well-known for the Kuramoto model regimes of full synchrony, full asynchrony, and integrable neutral quasiperiodic states, ensembles of nonlinearly coupled oscillators demonstrate two novel nontrivial types of partially synchronized dynamics: self-organized bunch states and self-organized quasiperiodic dynamics. The analysis based on the Watanabe-Strogatz ansatz allows us to describe the self-organized bunch states in any finite ensemble as a set of equilibria, and the self-organized quasiperiodicity as a two-frequency quasiperiodic regime. An analytic solution in the thermodynamic limit of infinitely many oscillators is also discussed. 相似文献
2.
R. Donner 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(3):349-361
Networks of interacting components are a class of complex systems that has attracted considerable interest over the last decades.
In particular, if the dynamics of the autonomous components is characterised by an oscillatory behaviour, different types
of synchronisation can be observed in dependence on the type and strength of interactions. In this contribution, we study
the transition from non-synchronised to synchronised phase dynamics in complex networks. The most common approach to quantify
the degree of phase synchronisation in such systems is the consideration of measures of phase coherence which are averaged
over all pairs of interacting components. However, this approach implicitly assumes a spatially homogeneous synchronisation process,
which is typically not present in complex networks. As a potential alternative, two novel methods of multivariate phase synchronisation analysis are considered: synchronisation cluster analysis (SCA) and the linear variance decay (LVD)
dimension method. The strengths and weaknesses of the traditional as well as both new approaches are briefly illustrated for
a Kuramoto model with long-range coupling. As a practical application, we study how spatial heterogeneity influences the transition
to phase synchronisation in traffic networks where intersecting material flows are subjected to a self-organised decentralised
control. We find that the network performance and the degree of phase synchronisation are closely related to each other and
decrease significantly in the case of structural heterogeneities. The influences of the different parameters of our control
approach on the synchronisation process are systematically studied, yielding a sequence of Arnold tongues which correspond
to different locking modes. 相似文献
3.
This Letter proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks simultaneously. By designing effective adaptive controllers, we achieve synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, an illustrative example is presented to demonstrate the application of the theoretical results. 相似文献
4.
Using a slightly simplified version of the integrate and fire model of a neural network with delay, I study the stability
of the phase-locked state dependent on the coupling between the neurons and especially on a delay time. The coupling between
neurons may be arbitrary. It is shown that the phase-locked state becomes less stable with increasing delay and that relaxation
oscillations occur.
Received 28 December 1999 and Received in final form 13 June 2000 相似文献
5.
It is commonly accepted that realistic networks can display not only a complex topological structure, but also a heterogeneous distribution of connection weights. In addition, time delay is inevitable because the information spreading through a complex network is characterized by the finite speeds of signal transmission over a distance. Weighted complex networks with coupling delays have been gaining increasing attention in various fields of science and engineering. Some of the topics of most concern in the field of weighted complex networks are finding how the synchronizability depends on various parameters of the network including the coupling strength, weight distribution and delay. On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state. Finally, an example is given as an illustration testing the theoretical results. 相似文献
6.
Q. Y. Wang Q. S. Lu G. R. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(2):255-261
The collective behaviour of a square-lattice
Hodgkin-Huxley neural network model with white noise is
investigated by numerical methods. It is found that for an
intermediate value of noise the Hodgkin-Huxley neurons in the
square lattice exhibit an ordered circular structure. However, as
the noise level increases, the ordered circular structures are
distorted, and eventually totally destroyed. Thereby, the
constructive role of appropriately pronounced random perturbations
in the studied network is revealed. Furthermore, it is shown that
as the diffusive coefficient increases, the typical width of the
spatial waves also increases accordingly, which results in a
decrease of the number of cycles by a given size of the spatial
grid. More interestingly, it is observed that the spatio-temporal
coherence resonance is enhanced as the diffusive coefficient is
increased. Finally, the dependence of the typical width and the
average period of the firing rate function on the diffusive
coefficient is studied. Results presented in this paper should
prove valuable for the understanding of information processing of
neural systems in the presence of noise. 相似文献
7.
G. A. Tsekouras A. Provata 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):107-111
We examine the fractal patterns arising in the Lattice Limit Cycle model, when it
is restricted on square and fractal lattices.
We show that, for processes taking place on regular 2d substrates, the
fractal dimensions depend on the kinetic constants and we have observed
a sharp phase-transition from uniform 2d spatial distributions (df=2)
when the kinetic parameters are near the Hopf bifurcation point, to a
inside the limit cycle region.
For processes taking place on substrates which contain inactive sites,
we observe nucleation
of homologous species around inactive regions leading to poisoning,
when the active sites are distributed in a fractal manner on the substrate.
This is less frequent in cases where the active sites are distributed
uniformly and randomly on the lattice leading, normally,
to non-trivial steady states. 相似文献
8.
Shihong Wang Junzhong Yang 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):81-92
Generalized synchronization in a drive-response Chua circuits is investigated. A cascade of transitions to GS is observed
with increasing the interaction strength. The mechanism on the
transitions to GS is given based on the asymptotic behaviors of response dynamics. 相似文献
9.
L. Wang H. P. Dai H. Dong Y. Y. Cao Y. X. Sun 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,61(3):335-342
This paper considers the problem of controlling
weighted complex dynamical networks by applying adaptive control
to a fraction of network nodes. We investigate the local and
global synchronization of the controlled dynamical network through
the construction of a master stability function and a Lyapunov
function. Analytical results show that a certain number of nodes
can be controlled by using adaptive pinning to ensure the
synchronization of the entire network. We present numerical
simulations to verify the effectiveness of the proposed scheme. In
comparison with feedback pinning, the proposed pinning control
scheme is robust when tested by noise, different weighting and
coupling structures, and time delays. 相似文献
10.
B. Wang T. Zhou Z. L. Xiu B. J. Kim 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(1):89-95
We numerically investigate how to enhance
synchronizability of coupled identical oscillators in complex
networks with research focus on the roles of the high level of
clustering for a given heterogeneity in the degree distribution.
By using the edge-exchange method with the fixed degree sequence, we
first directly maximize synchronizability measured by the
eigenratio of the coupling matrix, through the use of the so-called
memory tabu search algorithm developed in applied mathematics. The
resulting optimal network, which turns out to be weakly
disassortative, is observed to exhibit a small modularity. More
importantly, it is clearly revealed that the optimally
synchronizable network for a given degree sequence shows a very low
level of clustering, containing much fewer small-size loops than the
original network. We then use the clustering coefficient as an
object function to be reduced during the edge exchanges, and find it
a very efficient way to enhance synchronizability. We thus
conclude that under the condition of a given degree heterogeneity,
the clustering plays a very important role in the network synchronization. 相似文献
11.
Projective Synchronization in Drive--Response Networks via Impulsive Control 总被引:1,自引:0,他引:1 下载免费PDF全文
Impulsive projective synchronization in 1 +N coupled chaotic systems are investigated with the drive-response dynamical network (DRDN) model. Based on impulsive stability theory, some simple but less conservative criteria axe achieved for projective synchronization in DRDNs. Furthermore, impulsive pinning scheme is also adopted to direct the scaring factor onto the desired value. Numerical simulations on generalized chaotic unified system axe illustrated to verify the theoretical results. 相似文献
12.
Cellular fluids are systems consisting of a collection of fluid cells surrounded by thin liquid films. In this study, systems
composed of two different kinds of cells (i.e., filled with fluids A and B) immersed in a third fluid phase (a liquid C) have been examined. The object of the study is
a collection of polyhedra of fluid B separated by a thin film of liquid C (a host B/C network), modified by the insertion
of small droplets/bubbles of fluid A. Interfacial tensions acting along the A-C and B-C interfaces are assumed to be the only
driving forces determining the structure of the resulting mixed system. Different configurations of mixed A/B/C systems, formed
by the insertion of A singlets or doublets into the nodes, edges, films and interior parts of cells of the B/C network have
been analyzed in terms of the interfacial energy of the system. The possibility of spontaneous migration of cells A through
the B/C network and the possible final cell arrangements have been examined. 相似文献
13.
Y. Zhang H.A. Cerdeira G. Hu 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(1):97-102
A ring of diffusively coupled R?ssler oscillators, which can develop the conventional rotating wave from high-dimensional
chaos by increasing the coupling ɛ continuously is studied. The chaotic generator for the rotating wave emerges around ɛ =
ɛ, where the topological transition induced by the coupling not only changes the topological structure of all the oscillators,
which share a common strange attractor, but also changes them into being different from each other. Starting from this transition,
infinitely long range temporal correlation and spatial order in the style of antiphase state are established gradually, which
gives rise to the chaotic generator of the rotating wave.
Received 15 March 2001 相似文献
14.
A. B. Shapoval M. G. Shnirman 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(3):399-403
This paper considers a one-parameter family of sand-piles.
The family exhibits the crossover
between the models with deterministic and stochastic relaxation.
The mean pile height is used to describe the crossover.
The height densities corresponding to the models with relaxation
of both types approach one another as the parameter increases.
Relaxation is supposed to deal
with the local losses of grains by a fixed amount.
In that case the densities show a step-like behaviour
in contrast to the peaked shape
found in the models with the local loss of grains down
to a fixed level
[S. Lübeck, Phys. Rev. E 62, 6149 (2000)].
A spectral approach based on the long-run properties of the pile height
considers the models with deterministic and random relaxation
more accurately and
distinguishes between the two cases for admissible parameter values. 相似文献
15.
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
16.
A. Pluchino V. Latora A. Rapisarda 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):169-176
We discuss two models of opinion dynamics. We first present a brief review of
the Hegselmann and Krause (HK) compromise model in two dimensions,
showing that it is possible to simulate the dynamics
in the limit of an infinite number of agents by solving numerically a rate equation for
a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model,
which allows to study under which conditions a group of agents with a
different natural tendency (rate) to change opinion can find the
agreement. In the context of the this model, consensus is viewed as a synchronization
process. 相似文献
17.
S. Abe N. Suzuki 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(1):93-97
The network approach plays a distinguished role in
contemporary science of complex systems/phenomena. Such an approach has been
introduced into seismology in a recent work [S. Abe, N. Suzuki, Europhys.
Lett. 65, 581 (2004)]. Here, we discuss the dynamical property of
the earthquake network constructed in California and report the discovery
that the values of the clustering coefficient remain stationary before main
shocks, suddenly jump up at the main shocks, and then slowly decay following
a power law to become stationary again. Thus, the dynamical network approach
characterizes main shocks in a peculiar manner. 相似文献
18.
We propose a parametric approach to solve self-consistency equations that naturally arise in many-body systems described by nonlinear Fokker-Planck equations in general and nonlinear Vlasov-Fokker-Planck equations of Haissinski type in particular. We demonstrate for the Hess-Doi-Edwards model and the McMillan model of nematic and smectic liquid crystals that the parametric approach can be used to compute bifurcation diagrams and critical order parameters for systems exhibiting one or more than one order parameters. In addition, we show that in the context of the parametric approach solutions of the Haissinski model can be studied from the perspective of a pseudo order parameter. 相似文献
19.
We consider the collective dynamics for a multi-agent system with a virtual leader. The velocity of the leader is time-varying and the interconnection topology of position network is switching based on the distances between agents. To track the leader in flocking, a neighbour-based local piecewise smooth controller is proposed for each agent. Using the control method, all agent velocities asymptotically approach the desired velocity while collisions can be avoided between agents. Some simulation results are provided to demonstrate the theoretical results. 相似文献
20.
We investigate the dynamical response of the neuron system to a feeble external signal by using the Hindmarsh-Rose model, when the system is tuned below the first bifurcation point, which corresponds to the period-1 bursting state, and an external signal with a fixed period of about 170s is introduced to the system. It is found that to respond to the outside signal, the system changes from the period-1 state to a period-2 one with variation of the signal amplitude, indicating the occurrence of state-to-state transition (SST). Moreover, when a signal with different fixed periods is introduced, we can also find a similar transition between other states. Furthermore, the effect of the frequency of the signal on the transition is also discussed. These results may imply that SST plays a constructive role in information processing in neuron systems. 相似文献