Random talk: Random walk and synchronizability in a moving neighborhood network

Porfiri, Maurizio; Stilwell, Daniel J.; Bollt, Erik M.; Skufca, Joseph D.

doi:10.1016/j.physd.2006.09.016

Cited by 122 publications

(97 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Future efforts will be devoted to investigate the upper bound of degree d y and d θ to ensure the robust synchronization. In addition, particular interests have casted on stochastic synchronization with randomly switching topology, like representative stochastic models used in [15], [16], [18].…”

Section: Discussionmentioning

confidence: 99%

“…In [15], a connection graph stability method, also proposed by [20], is extended to a blinking model of small-world network in which both fixed 2K-nearest neighbor coupling and time-dependent on-off coupling are considered. In [16], each agent is assumed to be a random walker and random changes of network can be described by the change of agents' locations in the lattice where information can be transmitted only for agents in the same lattice. In [17], sufficient conditions are proposed for global synchronization with a fast and random switching network by using stochastic Lyapunov stability theory.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Han

Chesi

2014

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

Abstract-Robust synchronization problem is a key issue in chaotic circuits and nonlinear systems. This paper is concerned with robust synchronization problem of polynomial nonlinear system affected by time-varying uncertainties on topology, i.e., structured uncertain parameters constrained in a boundedrate polytope. Via partial contraction analysis, novel conditions, both for robust exponential synchronization and for robust asymptotical synchronization, are proposed by using parameterdependent contraction matrices. In addition, for polynomial nonlinear system, this paper introduces a new class of contraction matrix, i.e., homogeneous parameter-dependent polynomial contraction matrix (HPD-PCM), by which tractable conditions of linear matrix inequalities (LMIs) are provided via affine space parametrizations. Furthermore, the variant rate margin for robust asymptotical synchronization is, for the first time, proposed and investigated via handling generalized eigenvalue problems (GEVPs). A set of representative examples demonstrate the effectiveness of proposed method.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Han

Chesi

2014

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

show abstract

“…In particular, in [24] adaptive coupling was used to design communication channels able to compensate for parameter changes, while in [25] it was demonstrated that in a synchronization scheme where two Chua's circuits are pulse coupled, the switching frequency has to be larger than a threshold value to achieve synchronization. This behavior is now grounded on recent theoretical results for blinking networks [26,27], proving that under an assumption referred to as the fast switching hypothesis (FSH), when the link changes occur enough faster than the oscillator dynamics, the time-varying coupling can be studied by means of the time-average of the coupling matrix.…”

Section: Introductionmentioning

confidence: 89%

Synchronization of two Rössler systems with switching coupling

et al. 2016

View full text Add to dashboard Cite

In this paper, we study a system of two Rössler oscillators coupled through a time-varying link, periodically switching between two values. We analyze the system behavior with respect to the frequency of the switching. By applying an averaging technique under the hypothesis of a high switching frequency, we find that although each value of the coupling does not produce synchronization, switching between the two at a high frequency stabilizes the synchronization manifold. However, we also find windows of synchronization below the value predicted by this technique, and we develop a master stability function to explain the appearance of these windows. Spectral properties of the system are a useful tool for understanding the dynamical properties and the synchronization failure in some intervals of the switching frequency. Numerical and experimental results in agreement with the analysis are presented.

show abstract

“…the number of oscillators that are around i within a range d. When the agents move fast enough and the network topology changes very fast, we can apply the FSA [17,18,19,20], which consists in replacing the entries in the connectivity matrix in Eq. (3) by its time average.…”

Section: Model Settingsmentioning

confidence: 99%

“…On the one hand, when the network topology changes in a fast manner, a good approximation is to consider a network where the connections are represented by the probability of pairs of agents being connected. This is the so-called fast-switching approximation (FSA) [17,18,19,20]. On the other hand, when the population of agents is dense and arranged in a ring, the Fokker-Planck equation formalism has been used to describe the synchronization transition and the emergence of a spatial structure [21].…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis of Synchronization in Mobile Networks

Fujiwara

Kurths

Dı́az-Guilera

2011

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. We here analyze a system consisting of agents moving in a two-dimensional space that interact with other agents if they are within a finite range. Considering the motion and the interaction of the agents, the system can be understood as a network with a time-dependent topology. Dynamically, the agents are assumed to be identical oscillators, and the system will eventually reach a state of complete synchronization. In a previous work, we have shown that two qualitatively different mechanisms leading to synchronization in such mobile networks exist, namely global synchronization and local synchronization, depending on the parameters that characterize the oscillatory dynamics and the motion of the agents [1]. In this contribution we show that the spectral pattern differs between the two synchronization mechanisms. For global synchronization the spectrum is flat, which means that all eigenmodes contribute identically. For local synchronization, instead, the synchronization dynamics is determined mostly by the eigenmodes whose eigenvalues are close to zero. This result suggests that the global synchronization mechanism achieves fast synchronization by efficiently using the fast decaying eigenmodes (larger eigenvalues).

show abstract

Random talk: Random walk and synchronizability in a moving neighborhood network

Cited by 122 publications

References 29 publications

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Synchronization of two Rössler systems with switching coupling

Spectral Analysis of Synchronization in Mobile Networks

Contact Info

Product

Resources

About