Synchronization Probability in Large Complex Networks

Abstract

In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network structure and the local and coupling dynamics to synchronization stability. For large Erdös-Rényi networks, the obtained condition is translated into a lower bound on the probability of stability of synchrony. Our results show that the probability of stability quickly increases as the randomness crosses a threshold which for large networks is inversely proportional to the network size.

Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids

“…In this section, we assume that m 0 number of nodes are pinned. Similar to the case of single pinning, let the Laplacian matrix be permuted as (10) , the upper bound µ u is given in (12), and the lower bound µ l is the smallest positive root of the polynomials, α i (µ) i = 0, · · · , k − 1…”

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

“…Many systems in the real‐world can be modeled by networks, such as the neural networks, social network, electrical power grids, communication networks, the Internet, and the World Wide Web . Complex networks are made up of interconnected nodes interacting with others via a topology defined on the network edges . These nodes represent the individuals in the network with different meanings in different situations .…”

Stability analysis of network of similar-plants via feedback network

“…Recently the study of interacting dynamical systems as a network have drawn the attention of many scientists and engineers in various fields of physics, biology, and telecommunications [1]- [5]. The main stream of these efforts have been focused on stability of the dynamical flow in the network [3], [6].…”

“…The information or feedback network creates the cost of wiring or some other means of communications. Dealing with the problems of estimation errors and uncertainties of communication network are some of important challenges faced by this approach [5], [17]. Here first we try to separate the impact of network structures, such as degree of nodes, minimum and maximum degrees, on the stability from the local dynamics of nodes.…”

“…Here first we try to separate the impact of network structures, such as degree of nodes, minimum and maximum degrees, on the stability from the local dynamics of nodes. Since some of the networks in real the world depict the behavior reflected by random networks [5], [10], we focus on analyzing the network of plants with random connections in either feedback network or plant network. Assuming a random feedback network which is also a subnet of plant network, we calculate the probability of stability.…”