Dynamic Analysis and FPGA Implementation of a Fractional-Order Memristive Hopfield Neural Network with Hidden Chaotic Dual-Wing Attractors
S. He, Fei Yu, Rongyao Guo, Mingfang Zheng, Tinghui Tang, Jie Jin, Chunhua Wang
Abstract
To model the response of neural networks to electromagnetic radiation in real-world environments, this study proposes a memristive dual-wing fractional-order Hopfield neural network (MDW-FOMHNN) model, utilizing a fractional-order memristor to simulate neuronal responses to electromagnetic radiation, thereby achieving complex chaotic dynamics. Analysis reveals that within specific ranges of the coupling strength, the MDW-FOMHNN lacks equilibrium points and exhibits hidden chaotic attractors. Numerical solutions are obtained using the Adomian Decomposition Method (ADM), and the system’s chaotic behavior is confirmed through Lyapunov exponent spectra, bifurcation diagrams, phase portraits, and time series. The study further demonstrates that the coupling strength and fractional order significantly modulate attractor morphologies, revealing diverse attractor structures and their coexistence. The complexity of the MDW-FOMHNN output sequence is quantified using spectral entropy, highlighting the system’s potential for applications in cryptography and related fields. Based on the polynomial form derived from ADM, a field programmable gate array (FPGA) implementation scheme is developed, and the expected chaotic attractors are successfully generated on an oscilloscope, thereby validating the consistency between theoretical analysis and numerical simulations. Finally, to link theory with practice, a simple and efficient MDW-FOMHNN-based encryption/decryption scheme is presented.