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Global exponential stability of delayed periodic dynamical systems. (English) Zbl 1118.81479
Summary: We discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various ${L}^{p}$ $\left(1⩽p<\infty \right)$ norms. A general approach to investigate global exponential stability in terms of various ${L}^{p}$ ($1⩽p<\infty \right)$ norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria are given. More importantly, it is pointed out that sufficient conditions in terms of ${L}^{1}$ norm are enough and easy to implement in practice.
##### MSC:
 34K20 Stability theory of functional-differential equations 37C75 Stability theory 92B20 General theory of neural networks (mathematical biology)
##### Keywords:
neural networks; stability; global exponential convergence