A Second-Order Memristor-Based Rulkov Neuron: Design, Dynamical Analysis, and Application in Hierarchical Decryption of 3-D Model

Considering the extremely complex physiological environment within neurons, there is feedback from autapse currents as well as the influence of external electromagnetic radiation. In this article, a second-order memristor is constructed based on the definition of a generic memristor, which two intermediate variables are used to simultaneously model the effects of electromagnetic radiation and autapse on Rulkov neuron, called second-order memristor-coupled Rulkov neurons (SOM-Rulkov) neuron. The analysis of Lyapunov Exponent spectrum (LEs), bifurcation diagram, phase diagrams, and iterative diagrams with different parameters that SOM-Rulkov has various types of periodic and chaotic firing patterns and high complexity. In particular, homogeneous extreme multistability is demonstrated with different initial conditions, and the phenomenon is more suitable for image encryption. Furthermore, the SOM-Rulkov map is implemented on the DSP platform. Finally, the SOM-Rulkov map is applied to encrypt the 3-D model, which is essentially a sequence generated by homogeneous multistability and the vertex coordinates of the 3-D model for different position XOR operations. When decrypting, users with different levels of keys can access different visualizations. Experiments show that the scheme has strong security and low time cost.