Coexisting multi-stability of Hopfield neural network based on coupled fractional-order locally active memristor and its application in image encryption

Ding, Dawei; Xiao, Heng; Yang, Zongli; Luo, Honglin; Hu, Yongbing; Zhang, Xu; Liu, Yan

doi:10.1007/s11071-022-07371-0

Cited by 43 publications

(12 citation statements)

References 69 publications

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“…Based on the FO memristive synaptic-coupled neuron model, Xin et al [36] discussed its synchronization behaviors and found that the synchronization transition was affected by the fractional order. By using the coupled FO locally active memristor to simulate the synaptic crosstalk in Hopfield neural network, the HNN model with coupled locally active memristor has multi-stability under different fractional order and coupling coefficient, which was found by Ding et al [37]. Among many memristive neuron models, there is no research on memristive tabu learning neuron model in the field of FO calculus.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

et al. 2022

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External stimulus has an impact on the functional behavior of the biological nervous system, and appropriate stimulus helps the organism to maintain neural function. Inspired by this, the effects of different external stimuli on the dynamic behaviors of neuron model are studied in this paper. Firstly, a fractional-order(FO) memristor-coupled tabu learning two-neuron model whose equilibrium points are symmetric about the origin and unstable is constructed. The dynamic behaviors of this neuron model under different stimuli is further discussed, which are no external stimulus, external forced current stimulus and electromagnetic radiation (EMR) respectively. The neuron model without external stimulus has periodic attractors, but applying external stimulus to one of the neurons can produce abundant two-scroll chaotic attractors and multistability. Especially, when the neuron model is stimulated by EMR, it can generate hyperchaotic attractors that have not been observed in the tabu learning neuron model before. Besides, the transient transition behaviors of the model under different stimuli are also studied. Then, a pseudo-random number generator (PRNG) is designed and its random performance is tested with NIST suite. Finally, it is applied to voice encryption, and the result shows that it has good encryption effect. Therefore, it can be said that the FO memristor-coupled tabu learning two-neuron model has superior randomness and is suitable for chaotic-based engineering applications.

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Section: Introductionmentioning

confidence: 99%

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

et al. 2022

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“…Memristor-based neural network models can be classified into two categories: electromagnetic radiation neural network models [22,23] and memristive synaptic neural network models. [24,25] Among them, the electromagnetic radiation neural network model is a particular type of model that utilizes flux-controlled memristors to establish the correlation between magnetic field strength and membrane voltage in neural networks. The dynamic behaviors of neurons or neural networks are investigated in this model, focusing on the impact of external stimuli, including electromagnetic radiation and electric field stimulation.…”

Section: Introductionmentioning

confidence: 99%

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

Li 李,

He 何,

Yu 余

et al. 2024

Chinese Phys. B

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The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits. This study aims to develop a novel circuit simulation of a 3-neuron Hopfield neural network with coupled hyperbolic memristors through the modification of a single coupling connection weight. The bistable mode of the hyperbolic mHNN, characterized by the coexistence of asymmetric chaos and periodic attractors, is effectively demonstrated through the utilization of conventional nonlinear analysis techniques. These techniques include bifurcation diagrams, two-parameter maximum Lyapunov exponent plots, local attractor basins, and phase trajectory diagrams. Moreover, an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors. This method demonstrates significant benefits in correlation, information entropy, and resistance to differential attacks, providing strong evidence for its effectiveness in encryption. Additionally, an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN. The correctness of the circuit design is confirmed through Multisim simulations, which align with numerical simulations conducted in Matlab.

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“…Fractional-order differential operators, in comparison to integer-order ones, offer a more precise depiction of physical processes due to their non-local and memory properties, enhancing the adaptability of system processes [22]. The integration of traditional MNNs with fractional-order operators, resulting in fractional memristive neural networks (FMNNs) [23], has seen widespread application in image encryption [24], audio encryption [25], and secure communication [26]. Moreover, due to active device and amplifier switching speed limitations, neuron interactions often introduce time-varying delays, including discrete delays [27], distributed delays [28], and leakage delays [29].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

Wang,

Liu,

et al. 2024

Fractal Fract

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This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

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Coexisting multi-stability of Hopfield neural network based on coupled fractional-order locally active memristor and its application in image encryption

Cited by 43 publications

References 69 publications

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

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