Global Exponential Stability of Almost Periodic Solution for A Large Class of Delayed Dynamical Systems

Details Global Exponential Stability of Almost Periodic Solution for A Large Class of Delayed Dynamical Systems Global Exponential Stability of Almost Periodic Solution for A Large Class of Delayed Dynamical Systems

2006-10-30

arxiv.org/abs/math/0610920v1

Science in China Ser. A Mathematics 2005 Vol. 48 No. 8 1015—1026

Mathematics

Dynamical Systems

Scientific paper

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In 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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