Abstract
In the present study, we investigate the dynamics of shunting inhibitory cellular neural networks (SICNNs) with impulsive effects. We give a mathematical description of the chaos for the multidimensional dynamics of impulsive SICNNs, and prove its existence rigorously by taking advantage of the external inputs. The Li-Yorke definition of chaos is used in our theoretical discussions. In the considered model, the impacts satisfy the cell and shunting principles. This enriches the applications of SICNNs and makes the analysis of impulsive neural networks deeper. The technique is exceptionally useful for SICNNs with arbitrary number of cells. We make benefit of unidirectionally coupled SICNNs to exemplify our results. Moreover, the appearance of cyclic irregular behavior observed in neuroscience is numerically demonstrated for discontinuous dynamics of impulsive SICNNs.
Highlights
Bouzerdoum and Pinter [26] introduced and analyzed a class of cellular neural networks (CNNs), namely the shunting inhibitory cellular neural networks (SICNNs), which have been extensively applied in psychophysics, speech, perception, robotics, adaptive pattern recognition, vision and image processing [23, 24, 25, 32, 35, 41, 50, 80]
We develop the concept of Li-Yorke chaos to the multidimensional dynamics of impulsive SICNNs, and prove its presence rigorously
By establishing weak connections between SICNNs, we numerically demonstrate the appearance of near-periodic discontinuous chaos
Summary
Bouzerdoum and Pinter [26] introduced and analyzed a class of cellular neural networks (CNNs), namely the shunting inhibitory cellular neural networks (SICNNs), which have been extensively applied in psychophysics, speech, perception, robotics, adaptive pattern recognition, vision and image processing [23, 24, 25, 32, 35, 41, 50, 80]. Yang and Cao [106] considered the global exponential stability as well as the existence of a periodic solution for delayed cellular neural networks with impulsive effects based on the Halanay inequality, mathematical induction and a fixed point theorem. In the present study, we make use of chaotic external inputs and obtain chaos in the outputs of impulsive SICNNs with impacts subject to the cell and shunting principles. The emergence of near-periodic chaos in continuous-time systems without impulses was considered in the studies [15, 17] by means of weak chaotic perturbations applied to systems that possess stable periodic solutions. Discontinuous external inputs in a rectangular form are used in the first SICNN to provide the chaos
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
