Extreme multi-stability and microchaos of fractional-order memristive Rulkov neuron model considering magnetic induction and its digital watermarking application

This paper investigates a fractional-order Rulkov neuron model with discrete memristor under external electromagnetic radiation. The magnetic flux fluctuation crossing the neuron membrane is used to emulate the influence of electromagnetic radiation. The dynamics of the proposed fractional-order memristive Rulkov (FOMR) neural model are discussed using phase attractors, maximum Lyapunov exponents, bifurcation diagrams, etc. The FOMR neural model proposed exhibits not only extreme multi-stability and pervasive microchaos phenomena, but also demonstrates rich high-complexity dynamic behaviors. Digital implementations based on ARM are employed to validate the numerical simulation results. Finally, employing a method that combines Discrete Wavelet Transforms, Discrete Cosine Transforms, and chaotic index scrambling, a high-security digital watermarking scheme based on the FOMR neuron model for chaotic sequence encryption is proposed, which owns great keyspace and good encryption effect.