Local and global dynamical analysis of a second-order memristive digital filter model

To further promote the research in the field of discrete memristors, a discrete memristor is introduced into a two-dimensional chaotic map, which is a discrete model describing a second-order digital filter. A novel two-dimensional chaotic map is coined. The investigations on the local dynamics reveal the distribution patterns of dynamic, which are characterised on two-dimensional parameter planes. Two typical nonlinear phenomena, namely, resonance entrainments and cusp bifurcations, are identified explicitly by employing isocline method. Furthermore, the evolutions of basins of attraction are presented based on the tangency of stable and unstable manifolds. The critical curves are employed to derive global bifurcations, and further to demonstrate that the chaotic attractors are confined within specific boundaries. To show more evidences on the realizability of the map, several typical chaotic attractors are implemented on the DSP hardware platform.