Exponential periodic attractor of impulsive Hopfield-type neural network system with piecewise constant argument

• Main Authors: Manuel Pinto, Ricardo Torres, Daniel Sepúlveda
• Format: Article
• Language: English
• Published: University of Szeged 2018-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: piecewise constant arguments; cauchy and green matrices; hybrid equations; stability of solutions; gronwall's inequality; periodic solutions; impulsive differential equations; cellular neural networks
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6578

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.