A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability

Abstract

• A novel no-equilibrium HR neuron model with memristive electromagnetic induction is proposed. • This memristive HR neuron model can exhibit complicated memristor initial offset boosting dynamics. • The interesting phenomenon of hidden homogeneous extreme multistability is found. • Hardware experiments are performed to verify homogeneous coexisting hidden attractors. • A pseudo-random number generator with excellent randomness is designed based on memristor initial-controlled chaotic sequences. In this paper, a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic induction is proposed. This memristive HR neuron model exhibits complex memristor initial offset boosting dynamics, from which infinitely many coexisting hidden attractors sharing the same shape but with different positions can be generated, therefore breeding the interesting phenomenon of hidden homogeneous extreme multistability. The complicated dynamical behaviors are detailedly investigated via bifurcation diagrams, Lyapunov exponents , time series, attraction basins and spectral entropy (SE) complexity. Moreover, PSIM circuit simulations and DSP hardware experiments are carried out to demonstrate the theoretical analyses and numerical simulations. Finally, a pseudorandom number generator is also designed by using the memristor initial-controlled chaotic sequences extracted from the memristive HR neuron model. The performance analysis results show that these chaotic sequences can yield pseudorandom numbers with excellent randomness, which are more suitable for chaos-based engineering applications.