Synchronization of Stochastic Complex Dynamical Networks with Mixed Time-Varying Coupling Delays
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Synchronization of Stochastic Complex Dynamical Networks with Mixed Time-Varying Coupling Delays M. Syed Ali1 · M. Usha1 · Ahmed Alsaedi2 · Bashir Ahmad2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Synchronization of complex networks with mixed time-varying coupling delays and stochastic perturbation. We constructed a novel Lyapunov functional with triple integral terms. By applying Jensen’s inequality and Lyapunov stability theory stability conditions are derived to check the asymptotical stability of the concerned system. By employing the stochastic evaluation and Kronecker product delay-dependent synchronization criteria of stochastic complex dynamical networks are derived. By using the derived conditions control gain matrix is obtained. Finally, numerical results are presented to demonstrate the effectiveness and usefulness of the proposed results. Keywords Complex dynamical networks (CDNs) · Synchronization control · Linear matrix inequality · Lyapunov–Krasovskii functional · Time-varying coupling delays Mathematics Subject Classification 34D20 · 34K20 · 34K40
1 Introduction Over the past decade, complex systems [1] have received much attention from researchers. A complex system is a set of interconnected nodes, where the nodes and connections can be anything, such as mathematical, engineering, social, and economic science, nature and human societies. The networks arise in every place such as food courts, brain neuron networks, electric networks and World Wide Web (WWW) etc. [2–4]. In these networks complexities appear with regard to their topologies concerning nodes and coupled units of the networks. There are some critical and important phenomena in CDNs, which can be described by coupled differential equations [5]. One of the largest collective phenomena in complex dynamical networks is synchronization of all dynamical nodes inside the network which has covered a huge wide variety of researchers interest [6].
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M. Syed Ali [email protected]
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Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India
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Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
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M. S. Ali et al.
The synchronization phenomena is significant in normal-world networks, including synchronization at the net, and synchronization dealt with to organic neural networks [7–11]. Alternatively chaos synchronization is used in biology, chemistry, secret communication and cryptography, and some other nonlinear areas. A field of particular interest has been the control of synchronization of stochastic networks. Actually, synchronization is prominent in nature. For instance, synchronization of coupled oscillators can well clarify numerous characteristic wonders, for example, spatiotemporal confusion, auto waves, and winding waves [12]. Thus, the synchronization issue for CDNs has gotten expanding research consideration [13]. In complex networks
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