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Global exponential stability of almost periodic solution for a large class of delayed dynamical systems

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Abstract

Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with time-varying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems.

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Authors and Affiliations

  1. Key Laboratory of Nonlinear Mathematics Science of Ministry of Education, Fudan University, 200433, Shanghai, China

    Wenlian Lu & Tianping Chen

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  1. Wenlian Lu
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  2. Tianping Chen
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Correspondence to Tianping Chen.

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Lu, W., Chen, T. Global exponential stability of almost periodic solution for a large class of delayed dynamical systems. Sci. China Ser. A-Math. 48, 1015–1026 (2005). https://doi.org/10.1360/04ys0076

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  • DOI: https://doi.org/10.1360/04ys0076

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