Pinning a complex dynamical network via impulsive control. (English) Zbl 1234.05212
Summary: Complex dynamical networks are being studied across many fields of science and engineering today. The issue of controlling a network to the desired state has attracted increasing attention. In this Letter, we investigate the problem of pinning a complex dynamical network to the solution of an uncoupled system. Our strategy is to apply impulsive control to a small fraction of network nodes. Based on the Lyapunov stability theory, we prove that the theoretical results derived here are effective. In addition, a B-A scale-free network with 20 nodes is taken for illustration and verification.
MSC:
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 49N25 | Impulsive optimal control problems |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 34H10 | Chaos control for problems involving ordinary differential equations |
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