On the almost periodic solution of cellular neural networks with distributed delays.
By exponential dichotomy about differential equations, a formal almost periodic solution (APS) of a class of cellular neural networks (CNNs) with distributed delays is obtained. Then, within different normed spaces, several sufficient conditions guaranteeing the existence and uniqueness of an APS are proposed using two fixed-point theorems. Based on the continuity property and some inequality techniques, two theorems insuring the global stability of the unique APS are given. Comparing with known literatures, all conclusions are drawn with slacker restrictions, e.g., do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one, and the activation functions to be bounded, etc.; besides, all criteria are obtained by different ways. Finally, two illustrative examples show the validity and that all criteria are easy to check and apply.
Liu
Yiguang
Y
You
Zhisheng
Z
Cao
Liping
L
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D032701:Biomimetics / Q000379:methods*; D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010507:Periodicity; D009435:Synaptic Transmission / Q000502:physiology; D013997:Time Factors