Coupling Heterogeneous Neural Networks With Memristors

This paper proposes a novel approach for cascading Hopfield and Hindmarsh-Rose neural networks using memristive synapses. The model integrates two distinct neural networks, each consisting of two identical neurons. First, we design a memristor and analyze its memristive characteristics. We then develop the Hopfield and Hindmarsh-Rose networks with dual neurons, utilizing memristors to couple these sub-networks, forming a new four-neuron neural network. The equilibrium points and system stability are thoroughly analyzed. The dynamic behavior of the network is examined through bifurcation diagrams, two-parameter bifurcation plots, Lyapunov exponents, and phase diagrams, revealing phenomena such as chaos, periodicity, period-doubling bifurcations, and alternating-period chaos. To validate the numerical simulations, we implement the phase diagram on an STM32 hardware platform. Finally, we propose a DNA-based image encryption algorithm leveraging chaotic sequences generated by the network. The performance analysis of encrypted images demonstrates that the algorithm offers strong robustness during transmission and effective resistance against attacks, ensuring privacy and security.