Stochastic synchronization over a moving neighborhood network (original) (raw)
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Random talk: Random walk and synchronizability in a moving neighborhood network
Physica D: Nonlinear Phenomena, 2006
We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice. (D.J. Stilwell), bolltem@clarkson.edu (E.M. Bollt), jskufca@clarkson.edu (J.D. Skufca).
Synchronization in time-varying random networks with vanishing connectivity
Scientific Reports
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly, an extremely low instantaneous connectivity. We show that with strong coupling and sufficiently fast rewiring the network reaches partial synchronization even in the vanishing connectivity limit. In particular, we provide an approximate analytical argument, based on the comparison between the different characteristic timescales of our system in the low connectivity regime, which is able to predict the transition to synchronization threshold with satisfactory precision beyond the formal fast rewiring limit. We interpret our results as a qualitative mechanism for emergence of consensus in social communities. In particular, our result suggest that groups of individuals are capable of aligning their opinions under extremely sparse exchanges of views, which is reminiscent of fast communications that take place in the modern social media. Our results may also be relevant to characterize the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities.
Synchronization in Complex Networks With Stochastically Switching Coupling Structures
IEEE Transactions on Automatic Control, 2012
Synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed. A novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed. Some sufficient condition for a network with general time-varying coupling structure to reach complete synchronization is provided. Based on the general theorem, networks with stochastically switching coupling structures is investigated. In particular, two kinds of stochastic switching coupling networks are addressed: (a) independent and identically distributed switching processes and (b) Markov jump processes. In both cases, some sufficient condition for almost sure synchronization of the networks is given. Also, numerical simulations are provided to illustrate the theoretical results.
Synchronization over stochastically switching networks with imperfect prior information
Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications
This paper is concerned with output synchronization of nonlinear agents over a switching communication network. Under the assumption that the topology of the network is an i.i.d. stochastic process, a sufficient condition for synchronization was derived by Takaba (2012) in terms of a linear matrix inequality including the expected value of graph Laplacians. However, such an expected value may not be available in practical situations, we attempt to extend the above synchronization condition to the case where the expected Laplacian belongs to a prescribed polytopic set. Simulation results are also included.
Limitations and tradeoff in synchronization of large-scale stochastic networks
We study synchronization in scalar nonlinear systems connected over a linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network systems expressed in terms of the parameters of the nonlinear scalar dynamics, the second and largest eigenvalues of the mean interconnection Laplacian, and the variance of the stochastic uncertainty. The sufficient condition is independent of network size thereby making it attractive for verification of synchronization in a large size network. The main contribution of this paper is to provide analytical characterization for the interplay of roles played by the internal dynamics of the nonlinear system, network topology, and uncertainty statistics in network synchronization. We show there exist important tradeoffs between these various network parameters necessary to achieve synchronization. We show for nearest neighbor networks with stochastic uncertainty in interactions there exists an optimal number of neighbors with maximum margin for synchronization. This proves in the presence of interaction uncertainty, too many connections among network components is just as harmful for synchronization as the lack of connection. We provide an analytical formula for the optimal gain required to achieve maximum synchronization margin thereby allowing us to compare various complex network topology for their synchronization property.
Finite-time stochastic synchronization of complex networks
In this paper, we study the finite-time stochastic synchronization problem for complex networks with stochastic noise perturbations. By using finite-time stability theorem, inequality techniques, the properties of Weiner process and adding suitable controllers, sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks. The effects of control parameters on synchronization speed and time are also analyzed. The results of this paper are applicable to both directed and undirected weighted networks while do not need to know any information about eigenvalues of coupling matrix. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, the results of this paper are important. A numerical example shows the effectiveness of our new results.
Synchronization in Random Weighted Directed Networks
IEEE Transactions on Circuits and Systems I: Regular Papers, 2000
We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.
Synchronization of Dynamical Networks Under Sampling
In proceedings of the 2013 European Control Conference
Motivated by the increasing interest in networked multi-agent systems and the wide number of applications in decentralized distributed control of smart grids, we address the problem of synchronization when each node (e.g., a microgrid, a distributed generator) is modeled as a linear-time continuous system whose output measurements are sent through communication links. However, the inclusion of a communication infrastructure adds new challenges to control strategies and some problems may arise such as time delays, packet losses, sampling period, just to name a few. In this work, we consider that data is sampled with homogeneous sampling periods. Then, using the novel concept of average passivity, we define the conditions for synchronizability when all nodes are identical and unstable dynamics are present. Additionally, results are extended to the case of non-uniform agents, and some simulations of synchronization in smart grids are introduced.
Global Synchronization of Moving Agent Networks with Time-varying Topological Structure
Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012), 2012
The synchronization of moving agent networks with linear coupling in a two dimensional space is investigated. Base on the Lyapunov stability theory, a criterion for the synchronization is achieved via designed decentralized controllers. And, an example of typical moving agent network, having the Rössler system at each node, has been used to demonstrate and verify the design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.
The European Physical Journal B, 2009
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 p diff , while after a critical value p c diff the system synchronizes into a limit cycle with specific frequency, deviating non-trivially from the meanfield 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 p diff .