Neural Chaotic Oscillation: Memristive Feedback, Symmetrization, and Its Application in Image Encryption

The symmetry of neuron discharging has some relationship with the electrophysiological characteristics and dynamic behavior of a neuron, and has a close relation with the symmetry of ion channels, current balance, neuron type, synaptic transmission, and network effects. Among them, the feedback and interactions in the network have a particularly direct impact on the symmetrical discharge of a neuron element. This work introduces a memristor as a synapse into a neuron cell, taking the membrane potential back to ion channels, and therefore various symmetric firing behaviors of Hindmarsh-Rose (HR) neurons are observed, including chaos and various periodic firings. By further adjusting the feedback, coexisting symmetrical discharge of the neuron is achieved. Furthermore, the impact of frequency variations on the memristor synapse is analyzed, and thus the operating regimes of memristor and resistor are classified and discussed. Circuit simulations prove the neural chaotic firings along with their symmetrized discharging processes, demonstrating the effectiveness of symmetrical control of chaotic discharge. Finally, applying the symmetrical system to DNA image encryption can effectively protect the security of images.