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Global exponential stability of a class of retarded impulsive differential equations with applications. (English) Zbl 1197.34146

Summary: This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
92B20General theory of neural networks (mathematical biology)