Some novel double-scroll chaotic attractors in Hopfield networks

Zheng, Pengsheng; Zhang, Jianxiong

doi:10.1016/j.neucom.2010.02.015

Cited by 43 publications

(11 citation statements)

References 15 publications

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“…The authors present a numerical verification of the existence of a horseshoe in this system, for a certain parameter value. Lyapunov exponents spectrum, power spectrum, bifurcation diagrams, and topological horseshoe theory were used by Zheng and co-workers [5] to numerically investigate another three-neuron one-parameter chaotic Hopfield-type network with the hyperbolic tangent as the activation function. The existence of a horseshoe in the system was proved for a certain value of the variable parameter.…”

Section: Introductionmentioning

confidence: 99%

On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

SİLVA

Rech

2022

Communications in Advanced Mathematical Sciences

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In this work we report numerical results involving a certain Hopfield-type three-neurons network, with the hyperbolic tangent as the activation function. Specifically, we investigate a place of a two-dimensional parameter-space of this system where typical periodic structures, the so-called shrimps, are embedded in a chaotic region. We show that these structures are organized themselves as a spiral that coil up toward a focal point, while undergo period-adding bifurcations. We also indicate the locations along this spiral in the parameter-space, where such bifurcations happen.

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Section: Introductionmentioning

confidence: 99%

On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

SİLVA

Rech

2022

Communications in Advanced Mathematical Sciences

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“…Since the discovery of brain-like chaos in an HNN with six neurons [7], small HNN models have attracted considerable attention due to their abundant dynamical behaviors. Over the past decades, various chaotic behaviors including chaos [8][9][10][11] and hyperchaos [12][13][14] have been revealed based on different HNN models. Especially, in recent years, great progress in neuroscience and nonlinear theory has inspired an increasing enthusiasm in research on the complex dynamical behaviors in HNNs.…”

Section: Introductionmentioning

confidence: 99%

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Lin

Wang

Chen

et al. 2021

IEEE Trans. Circuits Syst. I

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Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

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“…The Hopfield network is one of the most typical ANNs, which consists of a number of fully-connected neuron units. In the Hopfield network, each unit is connected to all the other units, so the Hopfield network is a feedback network [31,32]. It is also a chaotic neural network.…”

Section: Introductionmentioning

confidence: 99%

Metasurface design by a Hopfield network: finding a customized phase response in a broadband

Zhu¹,

Qiu²,

Wang³

et al. 2020

J. Phys. D: Appl. Phys.

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In this paper we proposed a metasurface design method by finding out the meta-atoms through a Hopfield network. As part of the iterative design process, since the Hopfield network is capable of filtering out unreasonable designs with no need for going through full-wave simulation, the search for meta-atom patterns is reduced and undesired results are filtered effectively. To demonstrate the validity and reliability of this method, we searched meta-atoms that can achieve customized phase profiles in a broadband for achieving two functional metasurfaces, i.e., abnormal reflection and diffusive scattering. On that basis, the generated meta-atoms compose the phase profiles of the metasurfaces. By comparing the calculated, simulated and measured results, their consistency convincingly verifies the competency of this method. More importantly, this method provides an effective phase-search strategy to obtain desired phase responses intelligently in the field of functional metasurfaces design.

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Some novel double-scroll chaotic attractors in Hopfield networks

Cited by 43 publications

References 15 publications

On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Metasurface design by a Hopfield network: finding a customized phase response in a broadband

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