Synchronization of boundary coupled Hindmarsh–Rose neuron network

Phan, Chi; You, Yuncheng

doi:10.1016/j.nonrwa.2020.103139

Cited by 15 publications

(7 citation statements)

References 10 publications

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“…Here we consider the weak solutions of this initial value problem (2.5), cf. [6, Section XV.3] and the corresponding definition we presented in [25,26]. The following proposition claiming the local existence and uniqueness of weak solutions in time can be proved by the Galerkin approximation method.…”

Section: Fitzhugh-nagumo Neural Network With Boundary Couplingmentioning

confidence: 99%

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Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

Skrzypek

You

2020

Preprint

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In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. We analyze the dissipative dynamics and boundary coupling dynamics of the solution semiflow with sharp estimates. The exponential synchronization of this kind complex neural networks is proved under the condition that synaptic stimulation signal strength reaches a threshold quantitatively expressed.

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Section: Fitzhugh-nagumo Neural Network With Boundary Couplingmentioning

confidence: 99%

“…Beside synchronization of two coupled Hindmarsh-Rose neurons has been studied in [9,25]. Recently we have proved in [26] the asymptotic synchronization of the star-like Hindmarsh-Rose neural networks.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

Skrzypek

You

2020

Preprint

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“…Recently we proved results on the exponential synchronization of the boundary coupled Hindmarsh-Rose neural networks in [15,16] and the boundary coupled partly diffusive FitzHugh-Nagumo neural networks in [19].…”

Section: Introductionmentioning

confidence: 97%

Feedback Synchronization of FHN Cellular Neural Networks

Skrzypek¹,

You²

2020

Preprint

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“…Recently the authors proved results on the exponential synchronization for the boundary coupled Hindmarsh-Rose neuron networks in [23,24], the boundary coupled partly diffusive FitzHugh-Nagumo neural networks in [27], and the feedback synchronization of the one-dimensional FitzHugh-Nagumo CNN in [28].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of 2D Cellular Neural Networks with Boundary Feedback

Skrzypek,

Phan,

You

2020

Preprint

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In this work we propose a new model of 2D cellular neural networks (CNN) in terms of the lattice FitzHugh-Nagumo equations with boundary feedback and prove a threshold condition for the exponential synchronization of the entire neural network through the a priori uniform estimates of solutions and the analysis of dissipative dynamics. The threshold to be satisfied by the gap signals between pairwise boundary cells of the network is expressed by the structural parameters and adjustable. The new result and method of this paper can also be generalized to 3D and higher dimensional FitzHugh-Nagumo type or Hindmarsh-Rose type cellular neural networks.

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Synchronization of boundary coupled Hindmarsh–Rose neuron network

Cited by 15 publications

References 10 publications

Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

Feedback Synchronization of FHN Cellular Neural Networks

Exponential Synchronization of 2D Cellular Neural Networks with Boundary Feedback

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