Hysteresis bifurcation and application to delayed FitzHugh-Nagumo neural systems
نویسندگان
چکیده
منابع مشابه
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling.
Small lattices of N nearest-neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in an N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case N>2. Bifurcatio...
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Neurons are the central biological objects in understanding how the brain works. The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear differential equations. Because these equations are difficult to deal with, there also exist several simplified models, of which many exhibit polynomial-like non-linear...
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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....
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— We study the synchronized/unsynchronized transition as a function of the noise intensity which appears in a system of globally coupled FitzHugh– Nagumo units under the effect of white noise. By the use of the proper definition of an order parameter, we obtain numerically the phase diagram as a function of the noise intensity and coupling constant.
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We have studied the dynamical properties of finite N -unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Jpn. 75, 033001 (2006)]. In the AMM, original 2N -dimensional stochastic equations are transformed to eight-dimensional deterministic ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2021.125151