A discrete memristive cyclic Hopfield neural network with multi-cavity-like attractors and application in secure communication.

Discrete memristors with synapse-like properties play a significant role in elucidating the complex neurodynamic mechanisms of biological neural networks in the brain. This work presents a discrete memristive cyclic Hopfield neural network (DMCHNN), which integrates a novel discrete cosine memristor model for simulating mutual synaptic connections with a cyclic Hopfield neural network. Numerical analysis indicates that the system can control the chaotic range through amplitude modulation of the coupling strength k and weight w31, generating different numbers of multi-cavity-like hyperchaotic attractors under the regulation of k. By varying the initial value of the memristor, the system exhibits homogeneous and heterogeneous initial offset-boosting behaviors, accompanied by the coexistence of numerous homogeneous and heterogeneous attractors. Entropy performance evaluation further confirms that the system possesses excellent randomness. Furthermore, multi-cavity-like attractors produced by the system are successfully implemented on an FPGA hardware platform. Experimental results of the HE-DCSK communication system constructed based on DMCHNN demonstrate superior anti-noise performance compared to other chaotic maps.