Exotic dynamic behavior of the forced FitzHugh-Nagumo equations

Chou, Mo-Hong; Lin, Yu-Tuan

doi:10.1016/s0898-1221(96)00189-7

Cited by 19 publications

(8 citation statements)

References 7 publications

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“…The system (1) with I(t) periodic and b(t) constant was considered in [2]. A numerical study using the Poincaré map is made, and in particular the authors analyzed the consequences of imposing a sinusoidal perturbation of the form I 0 + I cos γt upon the base current.…”

Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

Periodic Solutions of a Periodic FitzHugh–Nagumo System

Llibre

Vidal

2015

Int. J. Bifurcation Chaos

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Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

Periodic Solutions of a Periodic FitzHugh–Nagumo System

Llibre

Vidal

2015

Int. J. Bifurcation Chaos

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“…By solving Equations (14)- (17) we get and so on and hence the above terms of the series (13) could be calculated. When we consider the series (13) with the terms (18)- (21) and suppose p = 1, we obtain the approximated solution of Equation (11) as follows:…”

Section: Examplementioning

confidence: 99%

Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses

Dehghan

Manafian

Saadatmandi

2010

Math. Meth. Appl. Sci.

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In this work, the homotopy perturbation method (HPM), the variational iteration method (VIM) and the Adomian decomposition method (ADM) are applied to solve the Fitzhugh-Nagumo equation. Numerical solutions obtained by these methods when compared with the exact solutions reveal that the obtained solutions produce high accurate results. The results show that the HPM, the VIM and the ADM are of high accuracy and are efficient for solving the Fitzhugh-Nagumo equation. Also the results demonstrate that the introduced methods are powerful tools for solving the nonlinear partial differential equations.

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“…Derived from [Hsu, 1987;Chou, 1993;Chou & Lin, 1996], the proposed global analysis provides a means to discretize and organize the phase space to reveal the set meeting the goal stated above. It begins with choosing a cubic region Ω = [a 1 , a 2 ] × [b 1 , b 2 ] × [c 1 , c 2 ] from the phase space, i.e.…”

Section: The Cell-to-cell Mappingmentioning

confidence: 99%

Oregonator-Based Simulation of the Belousov–zhabotinskii Reaction

Chou

Wei

Lin

2007

Int. J. Bifurcation Chaos

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Some observations are made on the Belousov-Zhabotinskii reaction simulated via the Field-Noyes model, also referred to as the Oregonator, and its modification. The simulation is performed with the aid of a cell-to-cell mapping for global analysis. Regarding the standard Oregonator, a two-dimension-like region in the three-dimensional phase space is detected showing the sensitive dependence of short-term ODE integrations on initial conditions. Trajectories with initial conditions closely located in this region may experience a phase lag if they eventually approach the same stable limit cycle connected with a subcritical Hopf bifurcation. When a flow term is added to the Oregonator, chaos can be brought about to mimic the experimental finding by suitably pleating the slow manifold. Coexistent attractors now may have a chaotic member and a fractal separatrix detected by the global analysis. The above mentioned sensitive region is found to play a significant role in shaping the pleating in order for chaos to happen in a manner analogous to the "screw-type" proposed by [Rössler, 1977] as one of the two prototypes for three-variable systems. Some relevant calculations of Lyapunov exponents, fractal dimensions and power spectra are also included.

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Exotic dynamic behavior of the forced FitzHugh-Nagumo equations

Cited by 19 publications

References 7 publications

Periodic Solutions of a Periodic FitzHugh–Nagumo System

Periodic Solutions of a Periodic FitzHugh–Nagumo System

Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses

Oregonator-Based Simulation of the Belousov–zhabotinskii Reaction

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