Abstract
In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.
Highlights
Competitive neural networks (CNNs), which are used to characterize the dynamics of cortical maps, have two types of state variables—the short-term memory variables (STM) that characterize the fast neural activity and the long-term memory (LTM) variables that characterize the slow unsupervised synaptic modifications
Mathematics 2019, 7, 321 to the best of our knowledge, there has been no paper published on the existence and global exponential stability of almost periodic solutions of neutral-type CNNs with mixed time-varying delays and leakage delays on time scales
Our main purpose of this paper is to study the existence and stability of almost periodic solutions of (1) on a new almost periodic time scale T which will be defined
Summary
Competitive neural networks (CNNs), which are used to characterize the dynamics of cortical maps, have two types of state variables—the short-term memory variables (STM) that characterize the fast neural activity and the long-term memory (LTM) variables that characterize the slow unsupervised synaptic modifications. To the best of our knowledge, so far, there have been few papers on the existence of almost periodic solutions for CNNs, especially for discrete-time CNNs. because time scale theory can unify continuous and discrete systems [21], we do not have to study discrete-time neural networks alone. Mathematics 2019, 7, 321 to the best of our knowledge, there has been no paper published on the existence and global exponential stability of almost periodic solutions of neutral-type CNNs with mixed time-varying delays and leakage delays on time scales. It is a challenging and important issue in theory and application.
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