Abstract
Based on the topological characteristics of small-world networks, a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties. To qualify the effects of uncertain parameters in the response networks, some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period. Meanwhile, the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network, respectively. The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks, and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.
Highlights
Synchronization has attracted significant attention in the last decade because of its extensive practical applications such as robot control, metabolic pathway, and aircraft formation
The studies in network synchronization mainly focus on the dynamic characteristics, e.g., modularity structure, hierarchy architecture, and small world effect, but only within one network
We aims to implement outer synchronization between two different spatiotemporal networks
Summary
Synchronization has attracted significant attention in the last decade because of its extensive practical applications such as robot control, metabolic pathway, and aircraft formation. Depending on the dynamics features of studied systems, researchers have proposed many control methods to obtain synchronization, e.g., adaptive synchronization, pinning synchronization, sliding mode synchronization[25,26,27,28]. In industrial processes, the systems have inertial related behaviors and measurement errors, which makes the variable structure control be accompanied by high frequency chattering under sliding mode dynamics[34]. For more complex network systems, the control method is improved by designing a developed fixed-time stable sliding surface and implementing synchronization of networks[37]. Spatiotemporal chaotic system has been widely used in practice such as modeling, control, and optimization Addressing these concerning issues, in this paper, two Watts-Strogatz (WS) small-world spatiotemporal networks with varied topologies are built. The high efficiency of the proposed synchronization approach is verified by numerical examples, even for WS smallworld spatiotemporal networks with different connection probabilities
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