The application of memristor in non-linear diffusive network is introduced. A charged-controlled memristor model is used in the quantitative study of pixel-to-pixel communication via a memristor. To quantitatively understand the behaviour of the system, the authors emphasised on two cells: master and slave. Information is launched from the master cell to the slave cell through a memristor and the dynamics, as well as, the saturation of the system is observed.

Many charge controlled models of memristor have been proposed for various applications. First, the original linear dopant drift model suffers discontinuities close to the memristor layer boundaries. Then, the nonlinear dopant drift model improves the memristor behavior near these boundaries but lacks physical meaning and fails for some initial conditions. Finally, we present a new model to correct these defects. We compare these three models in specific situations: (1) when a sine input voltage is applied to the memristor, (2) when a constant voltage is applied to it, and (3) how a memristor transfers charges in a circuit point of view involving resistance-capacitance network. In the later case, we show that our model allows for study of the memristor behavior with phase portraits for any initial conditions and without boundary limitations.

In this study, the authors consider a first step to apply memristor devices in a cellular non-linear network (CNN), where the advantages of the non-linearity, nanoscalability and memory effect could be taken into account to implement a 2D-CNN for signal and image processing-Memristors are used in the coupling mode to connect adjacent cells serially. They drive the analytical model describing the transmission of information from one cell to another via memristor, whose description in the ϕ-q plane is given, then improved to overcome the problem of discontinuities for some values of the charge q(t). The modified model is then chosen to be continued for all initial conditions and all parameters sets. Moreover, numerical simulations from SPICE and MATLAB software confirm the authors' analytical predictions.

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