Stability analysis in Lagrange sense for a non-autonomous Cohen-Grossberg neural network with mixed delays. (English) Zbl 1162.34338
Summary: The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen-Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.
MSC:
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34D40 | Ultimate boundedness (MSC2000) |
| 37B25 | Stability of topological dynamical systems |
| 37B55 | Topological dynamics of nonautonomous systems |
| 93C10 | Nonlinear systems in control theory |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
Keywords:
non-autonomous Cohen-Grossberg neural network; Lagrange stability; uniformly bounded; global exponential attractivity; mixed delaysReferences:
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