Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections, Rates and Inputs

Abstract

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.

Star Memristive Neural Network: Dynamics Analysis, Circuit Implementation, and Application in a Color Cryptosystem

“…It is well known that the human brain nervous system has abundant chaotic discharge behaviors [ 4 ], which are closely related to advanced intelligence. HNNs are considered to be the best example of studying the dynamics of the brain’s nervous system [ 5 , 6 ]. At the same time, many researchers have found that neural networks with chaotic behavior have a wide range of applications in many fields including associative memory, pattern recognition, and combinatorial optimization [ 7 , 8 ].…”