Dynamics for stochastic Fitzhugh–Nagumo systems with general multiplicative noise on thin domains
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7092
Abstract: This paper is devoted to studying the dynamics for stochastic Fitzhugh–Nagumo equations with general multiplicative noise on thin domains, where the noise is described by a general stochastic process instead of the usual Wiener process.… read more here.
Keywords: thin domains; general multiplicative; stochastic fitzhugh; multiplicative noise ... See more keywords
A bounded numerical solver for a fractional FitzHugh–Nagumo equation and its high-performance implementation
Sign Up to like & getrecommendations! Published in 2019 at "Engineering with Computers"
DOI: 10.1007/s00366-019-00902-1
Abstract: In this paper, we propose a high-performance implementation of a space-fractional FitzHugh–Nagumo model. Our implementation is based on a positivity- and boundedness-preserving finite-difference model to approximate the solutions of a Riesz space-fractional reaction-diffusion equation. The… read more here.
Keywords: implementation; fitzhugh nagumo; performance implementation; model ... See more keywords
Localized Patterns in a Three-Component FitzHugh–Nagumo Model Revisited Via an Action Functional
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-016-9557-z
Abstract: In this manuscript, we combine geometrical singular perturbation techniques and an action functional to revisit—and further study—the existence and stability of stationary localized structures in a singularly perturbed three-component FitzHugh–Nagumo model. In particular, the action… read more here.
Keywords: nagumo model; fitzhugh nagumo; three component; action functional ... See more keywords
Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model
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DOI: 10.1007/s10884-018-9694-7
Abstract: We analyse pinned front and pulse solutions in a singularly perturbed three-component FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit conditions for the existence and stability of these type of pinned solutions by… read more here.
Keywords: nagumo model; fitzhugh nagumo; three component; pinned solutions ... See more keywords
Mathematical Model of the Fitzhugh–Nagumo Hereditary Oscillator
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DOI: 10.1007/s10958-021-05250-4
Abstract: The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of a nerve impulse in a membrane. The model consists of an integro-differential equation with initial conditions (the Cauchy problem). The… read more here.
Keywords: hereditary oscillator; mathematical model; model; model fitzhugh ... See more keywords
Localized modulated wave solution of diffusive FitzHugh–Nagumo cardiac networks under magnetic flow effect
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-4617-z
Abstract: Motivated by often non-observance clinical effects attributed to some pathological heart diseases, we obtain in this paper the analytical solutions describing localized nonlinear excitations in an improved diffusive FitzHugh–Nagumo cardiac tissue model. The improved model… read more here.
Keywords: fitzhugh nagumo; localized modulated; nagumo cardiac; cardiac networks ... See more keywords
Local control of an array of the globally coupled oscillators
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DOI: 10.1007/s11071-019-05418-3
Abstract: Two control methods for stabilization of the steady states of the globally coupled second-order oscillators via local feedback are described. The first technique is based on the proportional feedback with a constant adjustable reference. The… read more here.
Keywords: control; nagumo oscillators; fitzhugh nagumo; globally coupled ... See more keywords
Chimera states in bipartite networks of FitzHugh–Nagumo oscillators
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DOI: 10.1007/s11467-017-0737-z
Abstract: Chimera states consisting of spatially coherent and incoherent domains have been observed in different topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh–Nagumo (FHN) oscillators… read more here.
Keywords: networks fitzhugh; bipartite networks; fitzhugh nagumo; chimera ... See more keywords
Long-Time Behavior of Non-Autonomous FitzHugh–Nagumo Lattice Systems
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DOI: 10.1007/s12346-020-00414-0
Abstract: In Abdallah (J Appl Math 3: 273–288, 2005), Boughoufala and Abdallah (Disc Cont Dyn Ays B), Li and Wang (J Math Anal Appl 325: 141–156, 2007), Vleck and Wang (Physica D 212: 317–336, 2005), Wang… read more here.
Keywords: nonlinear parts; fitzhugh nagumo; non autonomous; nagumo lattice ... See more keywords
Stochastic impact in Fitzhugh–Nagumo neural system with time delays driven by colored noises
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DOI: 10.1016/j.cjph.2017.11.014
Abstract: Abstract In this paper, stochastic behavior of FitzHugh–Nagumo neural system with two different kinds of time delays driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of… read more here.
Keywords: nagumo neural; system; fitzhugh nagumo; time delays ... See more keywords
The Γ-limit of traveling waves in the FitzHugh-Nagumo system
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.02.023
Abstract: Abstract Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization.… read more here.
Keywords: nagumo system; limit traveling; traveling waves; fitzhugh nagumo ... See more keywords