Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Zheng, Qianqian; Shen, Jianwei; Zhang, Rui; Guan, Linan; Xu, Yong

doi:10.3389/fphys.2022.936982

Cited by 8 publications

(9 citation statements)

References 34 publications

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“…We find the existence of an obvious irregular periodic oscillation phenomenon. Similar spatiotemporal pattern phenomena have also received attention in some work [40][41][42]. The parameter is ᾱ = 1.2 for (d), (e), and (f).…”

Section: Parameter Induces Spatiotemporal Pattern On Single-layer Net...mentioning

confidence: 58%

Pattern Formation in a Predator-Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Shi¹,

Zhou²,

Ye³

2023

Preprint

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With the rapid development of network science, Turing pattern on complex networks has attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator-prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing pattern is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing pattern. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing pattern is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing pattern, which is not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing pattern and spatiotemporal pattern. We believe that these findings contribute to a better understanding of self-organization on complex networks.

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Section: Parameter Induces Spatiotemporal Pattern On Single-layer Net...mentioning

confidence: 58%

Pattern Formation in a Predator-Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Shi¹,

Zhou²,

Ye³

2023

Preprint

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“…where ( x 0 , y 0 , z 0 ) ( Zheng et al, 2022) is the equilibrium point of system (2) without a network, and x 0 makes I ext = f ( x ) = − c + dx 2 + ax 3 − bx 2 + s ( x − x r ) + I ext + d 1 k i ( x 0 − x i ) hold. In addition, x 0 is the external stimulus from other neurons.…”

Section: Model Descriptionmentioning

confidence: 99%

“…The Hamilton energy balance of different functional neurons was discussed through the coupling strength, which contributes to designing functional assistive devices ( Zhang et al, 2022 ; Yu et al, 2023) . Although the HR model could explain the generation of short-term memory ( Zheng et al, 2022) , the utilization of energy should be further stated in short-term memory.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian energy in a modified Hindmarsh–Rose model

Zheng,

Xu,

Shen

2024

Front. Netw. Physiol.

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This paper investigates the Hamiltonian energy of a modified Hindmarsh–Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz’s theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

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“…When p increased to 0.01, neurons in the memory function areas fired, and the brain formed more vague memories ( Figures 4C , D , 5C , D ). Zheng et al ( 37 ) found that neurons exhibit different pattern dynamics with the change of network connection probability p in the study of the HR model. This conclusion is also confirmed in the study of multilayer networks.…”

Section: Simulationmentioning

confidence: 99%

“…Zheng et al studied the effect of noise on the bistable state of the FHN model and explained the biological mechanism of short-term memory by the pattern dynamics theory ( 36 ). They also studied the conditions of Turing pattern generation in the Hindmarsh-Rose (HR) model and found that collected current and outgoing current greatly influenced neuronal activity and used this to explain the mechanism of short-term memory generation ( 37 ). Wang and Shi proposed the time-delay memristive HR neuron model, found multiple modes and coherence resonance, and speculated that it might be related to the memory effect of neurons ( 38 ).…”

Section: Introductionmentioning

confidence: 99%

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

Wang

Shen

2023

Front. Psychiatry

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IntroductionThe study of brain function has been favored by scientists, but the mechanism of short-term memory formation has yet to be precise.Research problemSince the formation of short-term memories depends on neuronal activity, we try to explain the mechanism from the neuron level in this paper.Research contents and methodsDue to the modular structures of the brain, we analyze the pattern properties of the FitzHugh-Nagumo model (FHN) on a multilayer network (coupled by a random network). The conditions of short-term memory formation in the multilayer FHN model are obtained. Then the time delay is introduced to more closely match patterns of brain activity. The properties of periodic solutions are obtained by the central manifold theorem.ConclusionWhen the diffusion coeffcient, noise intensity np, and network connection probability p reach a specific range, the brain forms a relatively vague memory. It is found that network and time delay can induce complex cluster dynamics. And the synchrony increases with the increase of p. That is, short-term memory becomes clearer.

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Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Cited by 8 publications

References 34 publications

Pattern Formation in a Predator-Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Pattern Formation in a Predator-Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Hamiltonian energy in a modified Hindmarsh–Rose model

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

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