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Clarification and complement to "Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons" [PDF]
, 2015 In this note, we clarify the well-posedness of the limit equations to the mean-field $N$-neuron models proposed in Baladron et al. and we prove the associated propagation of chaos property. We also complete the modeling issue in Baladron et al.
Bossy, Mireille +2 more
core +6 more sources
Rocky Mountain Journal of Mathematics, 2011 Assuming the existence of ordered lower and upper solutions for \[ -\frac{d}{dt} \varphi(t,x,x(t),x'(t))=f(t,x,x(t),x'(t)) \quad \text{a.e. on } [0,1], \] the authors establish the existence of solutions to the above differential equation subject to general functional boundary conditions of the form \[ G(x(0),x(1),x,x'(0),x'(1))=(0,0), \] where ...
Mawhin, Jean, Thompson, H. B.
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Semigroups generated by pseudo-contractive mappings under the Nagumo condition
Journal of Differential Equations, 2008 This paper gives important results on existence on closed sets of a differential equation of type \(u'=Tu-u\) in Banach spaces. A weak tangency condition of Nagumo type is imposed. The operator \(T\) is demicontinuous and pseudo-contractive. Local as well as global solutions are investigated. Fixed points results are given as applications.
Hester, Anthony, Morales, Claudio H.
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Electronic Journal of Qualitative Theory of Differential Equations, 2011 This paper is concerned with a second-order nonlinear boundary value problem with a derivative depending nonlinearity and posed on the positive half-line. The derivative operator is time dependent.
Smail Djebali, S. Zahar
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New results and applications on the existence results for nonlinear coupled systems
Advances in Difference Equations, 2021 In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized nonlinear coupled boundary conditions satisfying the monotone assumptions.
Imran Talib +4 more
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Monostable-Type Travelling Wave Solutions of the Diffusive FitzHugh-Nagumo-Type System in 𝐑𝑁
Abstract and Applied Analysis, 2012 This paper is concerned with monostable-type travelling wave solutions of the diffusive FitzHugh-Nagumo-type system (FHN) in 𝐑𝑁 for the two components 𝑢 and 𝑣.
Chih-Chiang Huang
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Open Mathematics, 2023 This article discusses the existence of positive solutions for the system of second-order ordinary differential equation boundary value problems −u″(t)=f(t,u(t),v(t),u′(t)),t∈[0,1],−v″(t)=g(t,u(t),v(t),v′(t)),t∈[0,1],u(0)=u(1)=0,v(0)=v(1)=0,\left\{\begin{
Wang Dan, Li Yongxiang, Su Yi
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Frontiers in Physics, 2022 Synchronization of traveling waves in two rings of FitzHugh–Nagumo neurons is studied. Coupling between neurons within each ring is dissipative, while one between rings is memristive. Complete synchronization of waves in identical rings in the presence of an initial phase shift between wave processes and partial synchronization of waves in the case of ...
I. A. Korneev +5 more
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Dynamical mechanism of anticipating synchronization in excitable systems [PDF]
, 2004 We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing.
A. Hodgkin +9 more
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Indentical synchronization in complete networks of reaction-diffusion equations of FitzHugh-Nagumo
Ho Chi Minh City Open University Journal of Science - Engineering and Technology, 2018 Synchronization is a ubiquitous feature in many natural systems and nonlinear science. This paper studies the synchronization in complete network consisting of n nodes.
Phan Van Long Em
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