Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
|Number of page(s)||14|
|Published online||25 October 2019|
- D.C. Bell and B. Deng, Singular perturbation of N-front travelling waves in the FitzHugh–Nagumo equations. Nonlin. Anal. Real World Appl. 3 (2002) 515–541. [CrossRef] [Google Scholar]
- G.A. Carpenter, A geometric approach to singular perturbation problems with applications to nerve impulse equations. J. Differ. Equ. 23 (1977) 335–367. [Google Scholar]
- B. Datsko and V. Gafiychuk, Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems. B. Pol. Acad. Sci. Tech. Sci. 66 (2018) 411–418. [Google Scholar]
- B. Datsko, V. Gafiychuk and I. Podlubny, Solitary travelling auto-waves in fractional reaction–diffusion systems. Commun. Nonlin. Sci. Numer. Simul. 23 (2015) 378–387. [CrossRef] [Google Scholar]
- B. Deng, The existence of infinitely many traveling front and back waves in the FitzHugh–Nagumo equations. SIAM J. Math. Anal. 22 (1991) 1631–1650. [CrossRef] [MathSciNet] [Google Scholar]
- P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch. Ration. Mech. Anal. 65 (1977) 335–361. [Google Scholar]
- R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445–466. [CrossRef] [PubMed] [Google Scholar]
- C.K.R.T. Jones, Stability of the travelling wave solution of the FitzHugh-Nagumo system. Trans. Am. Math. Soc. 286 (1984) 431–469. [Google Scholar]
- H.P. McKean Jr, Nagumo’s equation. Adv. Math. 4 (1970) 209–223. [CrossRef] [Google Scholar]
- R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1–77. [Google Scholar]
- R. Metzler and J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37 (2004) R161–R208. [NASA ADS] [CrossRef] [Google Scholar]
- J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proc. Inst. Radio Eng. 50 (1962) 2061–2070. [Google Scholar]
- A.A. Nepomnyashchy and V.A. Volpert, An exactly solvable model of subdiffusion–reaction front propagation. J. Phys. A 46 (2013) 065101. [CrossRef] [MathSciNet] [Google Scholar]
- J. Rinzel and J.B. Keller, Traveling wave solutions of a nerve conduction equation. Biophys. J. 13 (1973) 1313–1337. [CrossRef] [PubMed] [Google Scholar]
- J. Rinzel and D. Terman, Propagation phenomena in a bistable reaction-diffusion system. SIAM J. Appl. Math. 42 (1982) 1111–1137. [Google Scholar]
- V.A. Volpert, Y. Nec and A.A. Nepomnyashchy, Exact solutions in front propagation problems with superdiffusion. Physica D 239 (2010) 134–144. [Google Scholar]
- V.A. Volpert, Y. Nec and A.A. Nepomnyashchy, Fronts in anomalous diffusion–reaction systems. Philos. Trans. Royal Soc. A 371 (2013) 20120179. [CrossRef] [Google Scholar]
- E. Yanagida, Stability of travelling front solutions of the FitzHugh-Nagumo equations. Math. Comput. Model. 12 (1989) 289–301. [Google Scholar]
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