# American Institute of Mathematical Sciences

June  2016, 21(4): 1119-1148. doi: 10.3934/dcdsb.2016.21.1119

## Impulsive SICNNs with chaotic postsynaptic currents

 1 Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey, Turkey

Received  December 2014 Revised  December 2015 Published  March 2016

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.
Citation: Mehmet Onur Fen, Marat Akhmet. Impulsive SICNNs with chaotic postsynaptic currents. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1119-1148. doi: 10.3934/dcdsb.2016.21.1119
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