Application of discrete memristors in logistic map and Hindmarsh–Rose neuron

Abstract

Continuous memristor (CM) has been widely designed and applied in chaotic and neuromorphic systems. However, discrete memristor (DM) and its application are less studied. This paper reports two kinds of generalized DM model based on sampling discretization of generalized CM model. It is found that the DM models can still retain the characteristics of the CM models. Based on the proposed DM models, the Logistic map (DM-L map) and two-dimensional (2D) discrete Hindmarsh–Rose neuron model (DM-HR model) are constructed. Through multiple numerical measures, it is found that DM-L map has linear fixed points, whose stability are only related to system parameter, and that DM-HR model does not have fixed point thus can generate hidden periodic and chaotic attractors. In particular, the coexistence of point and periodic attractors with different topological structures occur in DM-L map when different initial values are taken, which are rarely reported previously. At the same time, the chaotic region becomes wider when DM is introduced into Logistic map. Therefore, we believe that DM can effectively improve chaotic complexity of Logistic map. However, in addition to hidden complex discharge phenomenon, the coexistence of periodic and chaotic attractors with different positions and shapes are observed in DM-HR model. Finally, the DSP-based hardware platform is constructed to implement these maps, and the experimental results are consistent with the numerical simulation.