Shaoqi He

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.

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.

The memory characteristics and high nonlinearity of memristors make them ideal devices for simulating artificial synapses. The hyperbolic tangent function is a commonly used activation function in Hopfield neurons, where its activation gradient serves as a gain scaling parameter reflecting the response speed of neuronal electrical activity. This paper employs an exponential-type memristor as the activation gradient on the second neuron and proposes a novel method for integrating memristors with discrete coupled neural networks. Furthermore, the effect of the memristor’s gain on the hyperbolic tangent activation function is analyzed. Furthermore, a Discrete Hopfield Neural Network (DHNN) model with infinitely many equilibrium points is constructed by integrating a discrete magnetically controlled memristive model with sine and square functions as subsynapses of the first neuron. The results indicate that this DHNN can exhibit complex and diverse dynamical behaviors related to multiple system parameters, including rare hyperchaotic behavior characterized by four positive Lyapunov exponents, discharge mode transitions, and coexisting attractors phenomena. Based on these, an efficient and secure color image encryption scheme is designed, and extensive security analysis shows that the proposed scheme has strong security performance.

In comparison with dissipative chaos, conservative chaos is better equipped to handle the risks associated with the reconstruction of phase space due to the absence of attractors. This paper proposes a novel five-dimensional (5D) conservative memristive hyperchaotic system (CMHS), by incorporating memristors into a four-dimensional (4D) conservative chaotic system (CCS). We conducted a comprehensive analysis, using Lyapunov exponent diagrams, bifurcation diagrams, phase portraits, equilibrium points, and spectral entropy maps to thoroughly verify the system’s chaotic and conservative properties. The system exhibited characteristics such as hyperchaos and multi-stability over an ultra-wide range of parameters and initial values, accompanied by transient quasi-periodic phenomena. Subsequently, the pseudorandom sequences generated by the new system were tested and demonstrated excellent performance, passing all the tests set by the National Institute of Standards and Technology (NIST). In the final stage of the research, an image-encryption application based on the 5D CMHS was proposed. Through security analysis, the feasibility and security of the image-encryption algorithm were confirmed.

The hyperbolic tangent function is a commonly used activation function in Hopfield neurons, where its activation gradient serves as a gain scaling parameter reflecting the response speed of neuronal electrical activity. This paper proposes a novel method of integrating memristors with discretely coupled neural networks by using an exponential memristor as the activation gradient of Neuron 2, and analyzes the impact of its gain on the hyperbolic tangent activation function. Furthermore, a discrete magnetically controlled memristor model combined with sine and square functions is used as subsynapses of Neuron 1, resulting in a Discrete Hopfield neural network (DHNN) model with infinitely many equilibrium points. The results indicate that this DHNN can exhibit complex and diverse dynamical behaviors related to multiple system parameters, including rare hyperchaotic behavior characterized by four positive Lyapunov exponents, discharge mode transitions, and coexistence phenomena. Based on this, an efficient and secure color image encryption scheme is designed, and extensive security analysis shows that the proposed scheme has strong security performance.