Abstract We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate bifurcations in ordinary delay differential equations. apply method rigorously investigate these nonlocal orbit structures FitzHugh–Nagumo equation, extended Lorenz-84 model time-delay SI model.

Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four dimensional Hodgkin-Huxley equations. These oscillations were subsequently described by the two dimensional FitzHugh-Nagumo Equations in close agreement with the HodgkinHuxley theory. It is shown that the FitzHugh-Nagumo equations can to close approxima...

The (constrained) canonical reduction of four-dimensional self-dual Yang–Mills theory to two-dimensional Fitzhugh–Nagumo and the real Newell–Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh–Nagumo and Newell– Whitehead equations. The corresponding gauge potential Al and the ...

The Exp-function method can be used as an alternative to obtain analytic and approximate solutions of different types of differential equations. In this work Exp -function method is used to find exact solitary wave solutions for Fitzhugh-Nagumo equation. The method is straightforward and concise and its applications for Fitzhugh-Nagumo equation enable one to find exact traveling wave solutions....

A mathematical model describing the resistance in cell membrane and nerve fiber is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied. Most famous models, such as the Hodgkin-Huxley model, FitzHugh-Nagumo ...

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent dif...