Further Analysis of Global Synchronisation for Networks of Identical Cells with Delayed Coupling

2015 ◽  
Vol 5 (3) ◽  
pp. 238-255 ◽  
Author(s):  
Chun-Hsien Li ◽  
Ren-Chuen Chen
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Time Delays ◽  
Large Scale ◽  
Collective Motions ◽  
Delay Dependent ◽  
Homogeneous Linear ◽  
Theoretical Results

AbstractSynchronisation is one of the most interesting collective motions observed in large-scale complex networks of interacting dynamical systems. We consider global synchronisation for networks of nonlinearly coupled identical cells with time delays, using an approach where the synchronisation problem is converted to solving an homogeneous linear system. This approach is extended to fit networks under more general coupling topologies, and we derive four delay-dependent and delay-independent criteria that ensure the coupled dynamical network is globally synchronised. Some examples show that the four criteria are not mutually inclusive, and numerical simulations also demonstrate our theoretical results.

scholarly journals Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mingyue Li ◽  
Huanzhen Chen ◽  
Xiaodi Li
Keyword(s):  
Complex Networks ◽  
Time Delays ◽  
Large Scale ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Leader Following ◽  
Delay Dependent ◽  
Delayed Impulses ◽  
Impulsive Differential Inequality ◽  
Impulsive Disturbances

This paper studies the problem of leader-following synchronization for complex networks subject to delayed impulsive disturbances, where two kinds of time delays considered exist in internal complex networks and impulsive disturbances. Some delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs) by using the delayed impulsive differential inequality method. Moreover, a feedback controller is designed to realize desired synchronization via the established LMIs. Our proposed results show that the requirements of impulse intervals and impulse sizes are dropped, and delayed impulses and large scale impulses are allowed to coexist. Finally, some examples are given to show the effectiveness of the obtained results.

scholarly journals Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

Bifurcation, Synchronization, and Multistability of Two Interacting Networks with Multiple Time Delays

2016 ◽  
Vol 26 (09) ◽  
pp. 1650156 ◽  
Author(s):  
Xiaochen Mao
Keyword(s):  
Time Delays ◽  
Nearest Neighbor ◽  
Pitchfork Bifurcation ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Trivial Equilibrium ◽  
Dynamical Properties ◽  
Interacting Networks ◽  
Delay Dependent ◽  
Theoretical Results

This paper reveals the dynamical properties of two interacting neural networks with multiple couplings. Different time delays are introduced into the nearest-neighbor links and long-range connections in each layer and the couplings between different substructures. The delay-dependent and delay-independent stability and the oscillations bifurcated from the trivial equilibrium of the network are analyzed. The conditions of the existence of nontrivial equilibria and pitchfork bifurcation are discussed. Numerical simulations are performed to validate the theoretical results and interesting neuronal activities are observed, such as completely synchronous oscillations, three types of asynchronous oscillations, multiple switches between the rest states and different oscillations, coexistence of different oscillations, and coexistence of nontrivial equilibria and oscillations.

scholarly journals Analysis of a Stochastic Competitive Model with Distributed Time Delays and Jumps in a Polluted Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Taolin Zhang ◽  
Yuanfu Shao ◽  
Xiaowan She
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Time Delays ◽  
Polluted Environment ◽  
Persistence In Mean ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Lévy Jumps ◽  
Theoretical Results

In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results.

Cluster Mixed Synchronization of Complex Networks with Disturbance

2015 ◽  
Vol 719-720 ◽  
pp. 448-451
Author(s):  
Li Jie Zeng
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Bounded Disturbances ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, we investigate the cluster mixed synchronization scheme in time-varying delays coupled complex dynamical networks with disturbance. Basing on the community structure of the networks, some sufficient criteria are derived to ensure cluster mixed synchronization of the network model. Particularly, unknown bounded disturbances can be conquered by the proposed control. The numerical simulations are performed to verify the effectiveness of the theoretical results

scholarly journals Synchronizability of Multi-Layer Dual-Center Coupled Star Networks

2021 ◽  
Vol 9 ◽  
Author(s):  
Jian Zhu ◽  
Da Huang ◽  
Zhiyong Yu ◽  
Ping Pei
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Network Structure ◽  
Single Layer ◽  
Ring Networks ◽  
Laplacian Spectrum ◽  
Single Center ◽  
Stability Function ◽  
Star Networks ◽  
Theoretical Results

In the research on complex networks, synchronizability is a significant measurement of network nature. Several research studies center around the synchronizability of single-layer complex networks and few studies on the synchronizability of multi-layer networks. Firstly, this paper calculates the Laplacian spectrum of multi-layer dual-center coupled star networks and multi-layer dual-center coupled star–ring networks according to the master stability function (MSF) and obtains important indicators reflecting the synchronizability of the above two network structures. Secondly, it discusses the relationships among synchronizability and various parameters, and numerical simulations are given to illustrate the effectiveness of the theoretical results. Finally, it is found that the two sorts of networks studied in this paper are of the same synchronizability, and compared with that of a single-center network structure, the synchronizability of two dual-center structures is relatively weaker.

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