References
- A.R.A.Anderson and B.D.Sleeman, Wave front propagation and its failure in coupled systems of discrete bistable cells modelled by FitzHugh–Nagumo dynamics, Int. J. Bifurcat. Chaos5 (1995), pp. 63–74.
- D.G.Aronson, N.V.Mantzaris, and H.G.Othmer, Wave propagation and blocking in inhomogeneous media, Discrete Cont. Dyn. Syst.13 (2005), pp. 843–876.
- J.W.Cahn, J.Mallet-Paret, and E.S.Van Vleck, Traveling wave solutions for systems of ODE's on a two-dimensional spatial lattice, SIAM J. Appl. Math.59 (1999), pp. 455–493.
- A.Carpio and L.L.Bonilla, Pulse propagation in discrete systems of coupled excitable cells, SIAM J. Appl. Math.63 (2002), pp. 619–635.
- A.Carpio and L.L.Bonilla, Depinning transitions in discrete reaction–diffusion equations, SIAM J. Appl. Math.63 (2003), pp. 1056–1082.
- X.Chen, J.S.Guo, and C.C.Wu, Traveling waves in discrete periodic media for bistable dynamics, Arch. Ration. Mech. Anal.189 (2008), pp. 189–236.
- S.Coombes, G.J.Lord, and M.R.Owen, Waves and bumps in neuronal networks with axo-dendritic synaptic interactions, Physica D178 (2003), pp. 219–241.
- C.E.Elmer, Finding stationary fronts for a discrete Nagumo and wave equation: Construction, Physica D218 (2006), pp. 11–23.
- C.E.Elmer, The stability of stationary fronts for a discrete nerve axon model, Math. Biosci. Eng.4 (2007), pp. 113–129.
- C.E.Elmer and E.S.Van Vleck, Traveling waves solutions for bistable differential-difference equations with periodic diffusion, SIAM J. Appl. Math.61 (2001), pp. 1648–1679.
- C.E.Elmer and E.S.Van Vleck, Spatially discrete FitzHugh–Nagumo equations, SIAM J. Appl. Math.65 (2005), pp. 1153–1174.
- G.Fath, Propagation failure of traveling waves in discrete bistable medium, Physica D (1998), pp. 176–190.
- J.A.Feroe, Existence and stability of multiple impulse solutions of a nerve equation, SIAM J. Appl. Math.42 (1982), pp. 235–246.
- A.R.Humphries, B.E.Moore, and E.S.Van Vleck, Fronts for bistable differential-difference equations with inhomogeneous diffusion, SIAM J. Appl. Math.71 (2011), pp. 1374–1400.
- H.J.Hupkes and B.Sandstede, Traveling pulse solutions for the discrete FitzHugh–Nagumo system, SIAM J. Appl. Dyn. Syst.9 (2010), pp. 827–882.
- H.J.Hupkes and B.Sandstede, Stability of pulse solutions for the discrete FitzHugh–Nagumo system, Trans. Am. Math. Soc.365 (2013), pp. 251–301.
- J.P.Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math.47 (1987), pp. 556–572.
- T.J.Lewis and J.P.Keener, Wave-block in excitable media due to regions of depressed excitability, SIAM J. Appl. Math.61 (2000), pp. 293–316.
- J.Mallet-Paret, The Fredholm alternative for functional differential equations of mixed type, J. Dyn. Differ. Equ.11 (1999), pp. 1–48.
- J.Mallet-Paret, The global structure of traveling waves in spatially discrete dynamical systems, J. Dyn. Differ. Equ.11 (1999), pp. 49–128.
- H.McKean, Nagumo's equation, Adv. Math.4 (1970), pp. 209–223.
- S.Morfu, V.I.Nekorkin, J.M.Bilbault, and P.Marquié, Wave front propagation failure in an inhomogeneous discrete Nagumo chain: Theory and experiments, Phys. Rev. E66 (2002), 046127, 8 pp.
- J.Rinzel and J.B.Keller, Traveling wave solutions of a nerve conduction equation, Biophys. J.13 (1973), pp. 1313–1337.
- L.F.Shampine, R.C.Allen, and S.Pruess, Fundamentals of Numerical Computing, Wiley, New York, 1997, pp. 184–193.
- W.Shen, Traveling waves in time almost periodic structures governed by bistable non linearities. I. Stability and uniqueness, J. Differ. Equ.159 (1999), pp. 1–54.
- W.Shen, Traveling waves in time almost periodic structures governed by bistable non linearities. II. Existence, J. Differ. Equ.159 (1999), pp. 55–101.
- J.Sneyd and J.Sherratt, On the propagation of calcium waves in an inhomogeneous media, SIAM J. Appl. Math.57 (1997), pp. 73–94.
- G.Teschl, Mathematical Surveys and Monographs, Jacobi Operators and Completely Integrable Nonlinear Lattices, Vol. 72, American Mathematical Society, Providence, RI, 2000.
- A.Tonnelier, Wave propagation in discrete media, J. Math. Biol.44 (2002), pp. 87–105.
- A.Tonnelier, The McKean's caricature of the Fitzhugh–Nagumo model I. The space-clamped system, SIAM J. Appl. Math.63 (2002), pp. 459–484.
- A.Tonnelier, McKean caricature of the FitzHugh–Nagumo model: Traveling pulses in a discrete diffusive medium, Phys. Rev. E67 (2003), 036105, 9 pp.
- L.Truskinovsky and A.Vainchtein, Kinetics of martensitic phase transitions: Lattice model, SIAM J. Appl. Math.66 (2005), pp. 533–553.
- W.-P.Wang, Multiple impulse solutions to McKean's caricature of the nerve equation. I. Existence, Commun. Pure Appl. Math.41 (1988), pp. 71–103.
- W.-P.Wang, Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability, Commun. Pure Appl. Math.41 (1988), pp. 997–1025.
- J.Yang, S.Kalliadasis, J.H.Merkin, and S.K.Scott, Wave propagation in spatially distributed excitable media, SIAM, J. Appl. Math.63 (2002), pp. 485–509.