Results 11 to 20 of about 8,022 (162)
Discover Applied Sciences, 2023 <p>We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under adaptive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance's $(i,u)$-curve and the connectivity of the adaptive coupling network.
Ralf Köhl +3 more
openaire +1 more source
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model [PDF]
, 2012 We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials, in parameter regimes characterised by mixed-mode oscillations.
Birkhoff G +11 more
core +2 more sources
A Nagumo Condition for Ordinary Differential Equations [PDF]
Proceedings of the American Mathematical Society, 1976 A condition is given which guarantees that each solution of y ( n ) = f ( x , y , y ′ , … , y (
openaire +2 more sources
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
Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise [PDF]
, 2008 We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery ...
Augello, G., Spagnolo, B., Valenti, D.
core +4 more sources
MULTIPLE PERIODIC SOLUTIONS OF p-LAPLACIAN EQUATION WITH ONE-SIDE NAGUMO CONDITION [PDF]
Journal of the Korean Mathematical Society, 2008 In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.
Jian Jun Zhang +3 more
openaire +1 more source
Mathematics, 2023 This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions.
Feliz Minhós, Gracino Rodrigues
doaj +1 more source
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.
openaire +3 more sources
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
doaj +1 more source
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.
openaire +1 more source