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.

In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Parameter b was a key factor in regulating the dynamical behavior of the system, mainly affecting the strength and direction of the influence of $z_1$ on $z_2$. It was found that when the system parameter b was within a wide range of $[13,300]$, the system remained hyperchaotic throughout. Analytical establishment of multistability mechanisms was achieved through invariance analysis of the state variables under specific coordinate transformations. Furthermore, offset boosting control was realized by strategically modulating the fifth state variable, $z_5$. The FPGA-based experimental results demonstrated that attractors observed via an oscilloscope were in close agreement with numerical simulations. To validate the system’s reliability for cybersecurity applications, we designed a novel image encryption method utilizing this hyperchaotic model. The information entropy of the proposed encryption algorithm was closer to the theoretical maximum value of 8. This indicated that the system can effectively disrupt statistical patterns. Experimental outcomes confirmed that the proposed image encryption method based on the hyperchaotic system exhibits both efficiency and reliability.

Unlike conventional models that typically rely on a single memristive synapse, this study uniquely proposes a novel 5D fractional-order memristive Hopfield neural network (FOMHNN) modulated by dual memristors to simultaneously emulate internal synaptic plasticity and external electromagnetic radiation effects in brain-like computing. Analytically, the FOMHNN features multiple parallel lines of equilibria with double-zero eigenvalues, rigorously proving the generation of hidden attractors. The continuous dynamical behaviors are systematically evaluated using the Adomian Decomposition Method (ADM), revealing rich phenomena including transient chaos, grid multi-scroll hidden attractors, and frequency-controllable extreme multistability with fractal-like basin boundaries. The theoretical model is physically validated on a Field Programmable Gate Array (FPGA) platform, demonstrating high precision and ultra-low power consumption. To bridge theoretical dynamics with cryptographic applications, a novel pseudo-random number generator is designed. By incorporating a chaotic derivative extractor, the generated sequences significantly reduce topological periodicity, successfully passing all rigorous NIST SP 800-22 statistical tests. Furthermore, an adaptive color image encryption scheme is developed, utilizing bidirectional feedback diffusion and least significant bit (LSB) key embedding. Security analyses confirm that the cipher, under the fractional order $q=0.95$, achieves near-ideal information entropy, optimal resistance against differential attacks, with NPCR and UACI values reaching 99.6114% and 33.4910%, both extremely close to their theoretical ideals (99.6094% and 33.4635%), and robust resilience against noise. Ultimately, the FOMHNN provides a highly secure and physically realizable chaotic source for advanced secure communications.

In neuromorphic circuits, memristors are ideal devices for mimicking biological synapses, while fractional-order systems, described by fractional-order integrals and derivatives, can capture past, present, and future states, making them an ideal choice for modeling complex biological systems. This work proposes a dual-neuron fractional-order memristive Hopfield neural network (FOMHNN-DN), incorporating a single memristive synapse, to investigate the dynamics of fractional-order memristive neural networks. Research results show that the dynamics of FOMHNN-DN is profoundly influenced by the memristor’s internal parameters and the system’s fractional order. Furthermore, the initial conditions v1(0), v2(0), and ϕ(0) of FOMHNN-DN modulate attractor positions, demonstrating a special extreme multistability. Additionally, FOMHNN exhibits rare chaotic scroll-growth attractors and burst-firing modes, both of which are modulated by initial offset-boosted effects, potentially yielding infinite dynamic variations. Finally, based on the scroll-growth situation, FOMHNN-DN is discretized using the Adomian decomposition method and implemented on a field- programmable gate array for hardware validation. By exploring FOMHNN-DN, this work lays a foundation for further research into biomimetic networks with complex nonlinear dynamic behaviors and their applications.