Resonance induced by mixed couplings in a three-node motif

Liu, Cong; Zhang, Xiyun; Liang, Xiaoming

doi:10.1007/s11071-020-05893-z

Cited by 4 publications

(2 citation statements)

References 36 publications

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“…In this formulation, an isolated FHN neuron is both excitable and bistable with two fixed points (x * 1 , y * 1 ) = (0.89, 0.04) and (x * 2 , y * 2 ) = (0.11, −0.04). To model a subthreshold signal, the amplitude and frequency are fixed to A = 0.01 and ω = π/5, respectively, as the reference [54] suggests, so that each neuron cannot generate spikes but can only oscillate slightly around the two fixed points. The time step of simulations is ∆t = 0.001 and the signal response can be revealed by the spectral amplification factor Q as well, in which X(t) represents the collective activity of the fast membrane potential.…”

Section: B Excitable Fhn Neuronsmentioning

confidence: 99%

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Resonance induced by higher-order coupling diversity

Liu¹,

Wang²,

Wu³

et al. 2022

Preprint

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The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be straightforwardly extended to the linear ones. In present work, we introduce the standard deviation of dynamic behavior for the interacting group to complement the higher-order effect that beyond pairwise in diffusive coupling. By doing so, the higher-order effect can be flexibly extended to the linearly coupled system. We leverage this modelization to embrace the influence of heterogeneous higher-order coupling, including promoting and inhibiting effects, on the signal response for two conventional models, the globally coupled overdamped bistable oscillators and excitable FitzHugh-Nagumo neurons. Particularly, we numerically and analytically reveal that the optimal signal response can be obtained by an intermediate degree of higher-order coupling diversity for both systems. This resonant signal response stems from the competition between dispersion and aggregation induced by heterogeneous higher-order and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in linearly coupled systems.

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Section: B Excitable Fhn Neuronsmentioning

confidence: 99%

“…For simplicity, we assume Ṁ = 0 and ∆ = 0 by using the approximation of adiabatic elimination [54]. Then, the ensemble dynamics are read as Ṡ = −(0.5 + 3M 2 )S + 1.5(S 2 + M 2 ) − S 3…”

Section: B Excitable Fhn Neuronsmentioning

confidence: 99%

Resonance induced by higher-order coupling diversity

Liu¹,

Wang²,

Wu³

et al. 2022

Preprint

Self Cite

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Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron

Guan

Zhao

2021

Nonlinear Dyn

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Double resonance induced by group coupling with quenched disorder

Liu

Wang

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Results show that the astrocytes can not only listen to the talk of large assemble of neurons but also give advice to the conversations and are significant sources of heterogeneous couplings as well. In the present work, we focus on such regulation character of astrocytes and explore the role of heterogeneous couplings among interacted neuron–astrocyte components in a signal response. We consider reduced dynamics in which the listening and advising processes of astrocytes are mapped into the form of group coupling, where the couplings are normally distributed. In both globally coupled overdamped bistable oscillators and an excitable FitzHugh–Nagumo (FHN) neuron model, we numerically and analytically demonstrate that two types of bell-shaped collective response curves can be obtained as the ensemble coupling strength or the heterogeneity of group coupling rise, respectively, which can be seen as a new type of double resonance. Furthermore, through the bifurcation analysis, we verify that these resonant signal responses stem from the competition between dispersion and aggregation induced by heterogeneous group and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in coupled systems with quenched disorder.

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Resonance induced by mixed couplings in a three-node motif

Cited by 4 publications

References 36 publications

Resonance induced by higher-order coupling diversity

Resonance induced by higher-order coupling diversity

Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron

Double resonance induced by group coupling with quenched disorder

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