Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System
نویسندگان
چکیده
منابع مشابه
Homoclinic Orbits of the FitzHugh-Nagumo Equation: The Singular-Limit
The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcati...
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The simplest models used to describe physical systems are often linear. However, several natural phenomena can only be accurately modeled by relatively complex nonlinear systems of equations. There is a wealth of interesting dynamics displayed by systems consisting of nonlinear elements, for example systems in which the dynamics depend delicately on the initial conditions, viz, chaos, and syste...
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This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional vector field depending upon system parameters of the FitzHugh-Nagumo model and the wave speed. Champneys et al. [A.R. Champneys, V. Kirk, E. Knobloch, B.E. Oldeman, and J. Sneyd, When Shilnikov meets Hop...
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In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure ν associated with the transition semi...
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An excitable medium has two key properties: a sufficiently large stimulus provokes an even bigger response (excitability), and immediately following a stimulus the medium cannot be excited (refractoriness). A large class of biological systems from cardiac tissue to slime mold are examples of excitable media. FitzHugh Nagumo (FHN) is the canonical model of excitable media. Its two variables are ...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2018
ISSN: 1536-0040
DOI: 10.1137/16m1080707