Memristive CNN with multi-butterfly attractors: Mathematical modeling, dynamics analysis and application in secure communication

Since the introduction of memristors into cellular neural networks (CNN), various memristive CNNs (MCNNs) have been constructed to investigate complex neuronal dynamics. However, butterfly attractor dynamics has not been reported in this context. To address this gap, this paper proposes a novel MCNN model incorporating two memristive systems within a single neuron to simulate two different electromagnetic induction effects. The system’s chaotic dynamics is thoroughly analyzed using bifurcation diagrams, Lyapunov exponents, and attraction basins. Results demonstrate that the proposed MCNN exhibits abundant butterfly attractor dynamics, including double-wing, multi-wing, and infinitely many coexisting double-wing butterfly attractors. Particularly, varying a control parameter in the second memristive system alters the number of multi-butterfly attractors, while modifying its initial condition shifts the positions of coexisting double-wing butterfly attractors, revealing clear multistability. Field Programmable Gate Array (FPGA)-based hardware experiments further validate these complex dynamical behaviors. Owing to these properties, the presented MCNN is well-suited for secure communication. To demonstrate its practical value, a novel encryption scheme tailored for the Internet of Vehicles (IoV) is designed and rigorously evaluated. Security analysis confirms that the designed encryption scheme provides strong robustness and high security in image encryption.