A discrete Chialvo–Rulkov neuron network coupled with a novel memristor model: Design, Dynamical analysis, DSP implementation and its application

In this paper, a novel discrete flux-controlled memristor model combining square and cosine function is proposed and its properties are analyzed. Then, the discrete memristor is used to couple discrete Chialvo and Rulkov neuron forming a simple neuron network. The memristive coupled bi-neuron(C-M-R) map is constructed to simulate the connection of two different neurons by a synaptic in biological organizations. The equilibrium of this discrete map is studied. Dynamical behaviors of the C-M-R map are studied through a variety of methods with different parameters. The analysis methods adopted include phase diagram, iterative diagram, bifurcation diagram, Lyapunov Exponent spectrum(LEs), and Spectral Entropy(SE) complexity. Multiple types of hyperchaotic, chaotic, periodic attractors are observed in the C-M-R map. Various hidden firing modes and coexisting firing modes also exist in the map. Furthermore, state transition and attractor coexistence concerning different types of hyperchaos are found. The DSP hardware implementation is accomplished, proving the physical feasibility of the C-M-R map. Finally, the map is used in a simple image encryption scheme. This research imitates the principle of biological neuron coupling and can be applied to secrecy and encryption systems.