Two-neuron-based non-autonomous memristive Hopfield neural network: Numerical analyses and hardware experiments

Xu, Quan; Song, Zhe; Bao, Han; Chen, Mo; Bao, Bocheng

doi:10.1016/j.aeue.2018.09.017

Cited by 72 publications

(27 citation statements)

References 32 publications

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“…Very recently, several research works have been carried out on the dynamic analysis of some particular classes of HNNs among with those with fixed activation gradients and those with variable activation gradients [ 12 – 15 , 20 , 38 ]. From some of these works summarized in Table 8 , it has been found that the investigated models were the phenomenon of the multistability characterized by the coexistence of several firing patterns for the same set of the synaptic weights by starting from different initial conditions.…”

Section: Comparative Analyses and Discussionmentioning

confidence: 99%

“…In other words, the term megastable has been used for systems with countable infinite attractors [ 36 ], in contrast to extreme multi-stability which is related to non-countable infinite attractors. The coexistence of multiple attractors including up to four disconnected found by Bao et al [ 12 , 15 , 37 ]. Likewise coexistence of up to six disconnected attractors as well as antimonotonicity phenomenon is found by Njitacke et al in some classes of 4D HNN in [ 13 , 14 ] and bursting oscillations [ 27 ] discovered by Bao et al in a model of two-neuron-based non-autonomous memristive Hopfield neural network.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, several works have been focused on the investigation of the multistable property of the HNN [ 12 – 15 ]. Recall that multistability in HNNs means the coexistence of several stable states for the same set of synaptic weight matrix by starting the evolution of the model from different initial conditions [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

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Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Njitacke

Doubla

Tsafack

et al. 2020

Neural Comput & Applic

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In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.

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Section: Comparative Analyses and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Njitacke

Doubla

Tsafack

et al. 2020

Neural Comput & Applic

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“…e memristor that had been postulated as the fourth basic circuit element in 1971 by Chua [16] is a two-terminal passive electronic element described by nonlinear constitutive relation of charge q and flux φ and was for the first time fabricated in 2008 by Williams's group of HP Labs [17]. Currently, the modeling of basic memristor circuits [18,19], the physical realization of all kinds of memristors and memristive systems [20,21], the design and analysis of memristor-based application circuits [22,23], etc. are attracting much attention in engineering communities.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Wan

Zhou

et al. 2020

Complexity

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In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system.

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“…Amanda et al, 2012 [8] showed that Rossler model under influence of external sinusoidal force may able to generate hyper chaos and both chaos-order. [9] exploited two-neuron based non-autonomous memristive Hopfield neural network to investigate dynamical behaviors including bursting. Recently, Ngo Mouela et al, 2019 [10] exploited a simple nonautonomous Jerk system with generalized nonlinearity to investigated rich dynamical behaviors including hyperchaos, chaos, intermittency and coexistence of multiple attractors.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an Optically Injected Diode Laser Subject to Periodic Perturbation: Occurrence of a Large Number of Attractors, Bistability and Metastable Chaos

Tchinda¹,

Njitacke²,

Fozin³

et al. 2019

CSSP

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It is well known that during a certain interval of time, a molecule of gas in the beam path from the pump laser (master) to the injected laser (slave) can decrease the power injected [1]. In this contribution, we consider a well-known rate equation model of semiconductor laser to explore numerically the effect of a periodic perturbation from the pump laser (master) on the dynamical behavior of the injected laser (slave). Using nonlinear diagnostic tools such bifurcation diagrams, graph of maximum Lyapunov exponent, phase portraits, Poincare sections, basin of attraction and two parameter diagrams, the dynamical behavior of the model is analyzed in terms of its parameters. The coexistence of periodic and chaotic attractors as well as the occurrence of ten different attractors (symmetric and asymmetric) and transient chaos are demonstrated. Finally, PSpice simulations are performed to support numerical results.

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Two-neuron-based non-autonomous memristive Hopfield neural network: Numerical analyses and hardware experiments

Cited by 72 publications

References 32 publications

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Dynamics of an Optically Injected Diode Laser Subject to Periodic Perturbation: Occurrence of a Large Number of Attractors, Bistability and Metastable Chaos

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