Exponential periodic attractor of impulsive Hopfield-type neural network system with piecewise constant argument. (English) Zbl 1413.34224
Summary: In this paper, we study a periodic impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Under general conditions, existence and uniqueness of solutions of such systems are established using ergodicity, Green functions and Gronwall integral inequality. Some sufficient conditions for the existence and stability of periodic solutions are shown and a new stability criterion based on linear approximation is proposed. Examples with constant and non-constant coefficients are simulated, illustrating the effectiveness of the results.
MSC:
34K13 | Periodic solutions to functional-differential equations |
34K20 | Stability theory of functional-differential equations |
34K34 | Hybrid systems of functional-differential equations |
34K45 | Functional-differential equations with impulses |
92B20 | Neural networks for/in biological studies, artificial life and related topics |