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Complexity is the undeniable part of the natural systems providing them with unique and wonderful capabilities. Memristor is known to be a fundamental block to generate complex behaviors. It also is reported to be able to emulate synaptic long-term plasticity as well as short-term plasticity. Synaptic plasticity is one of the important foundations of learning and memory as the high-order functional properties of the brain. In this study, it is shown that memristive neuronal network can represent plasticity phenomena observed in biological cortical synapses. A network of neuronal units as a two-dimensional excitable tissue is designed with 3-neuron Hopfield neuronal model for the local dynamics of each unit. The results show that the lattice supports spatiotemporal pattern formation without supervision. It is found that memristor-type coupling is more noticeable against resistor-type coupling, while determining the excitable tissue switch over different complex behaviors. The stability of the resulting spatiotemporal patterns against noise is studied as well. Finally, the bifurcation analysis is carried out for variation of memristor effect. Our study reveals that the spatiotemporal electrical activity of the tissue concurs with the bifurcation analysis. It is shown that the memristor coupling intensities, by which the system undergoes periodic behavior, prevent the tissue from holding wave propagation. Besides, the chaotic behavior in bifurcation diagram corresponds to turbulent spatiotemporal behavior of the tissue. Moreover, we found that the excitable media are very sensitive to noise impact when the neurons are set close to their bifurcation point, so that the respective spatiotemporal pattern is not stable.

Investigation of Cortical Signal Propagation and the Resulting Spatiotemporal Patterns in Memristor-Based Neuronal Network