Carpio Rodríguez, Ana María (2005) Wave trains, self-oscillations and synchronization in discrete media. Physica D-Nonlinear Phenomena, 207 . pp. 117-136. ISSN 0167-2789
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We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.
|Uncontrolled Keywords:||Nonlinear waves; Oscillators; Discrete media; Excitable media; Wave trains; Propagation failure; Relaxation oscillations; Synchronization; Pattern formation|
|Subjects:||Sciences > Physics > Mathematical physics|
 A.R.A. Anderson, B.D. Sleeman,Wave front propagation and its failure in coupled systems of discrete bistable cells modelled by FitzHugh- Nagumo dynamics, Int. J. Bif. Chaos 5 (1995) 63–74.
 G.W. Beeler, H.J. Reuter, Reconstruction of the action potential of ventricular mycardial fibers, J. Physiol. 268 (1977) 177–210.
 C.M. Bender, S.A. Orszag, Advanced Mathematical Methods For Scientists and Engineers, McGraw-Hill, 1978.
 L.L. Bonilla, H.T. Grahn, Non-linear dynamics of semiconductor superlattices, Rep. Prog. Phys. 68 (2005) 577–683.
 V. Booth, T. Erneux, Understanding propagation failure as a slow capture near a limit point, SIAM J. Appl. Math. 55 (1995) 1372–1389.
 J.W. Cahn, Theory of crystal growth and interface motion in crystalline materials, Acta Metall. 8 (1960) 554–562.
 A. Carpio, S.J. Chapman, S. Hastings, J.B. McLeod, Wave solutions for a discrete reaction-diffusion equation, Eur. J. Appl. Math. 11 (2000) 399–412.
 A. Carpio, L.L. Bonilla, Depinning transitions in discrete reaction-diffusion equations, SIAM J. Appl. Math. 63 (3) (2003) 1056–1082.
 A. Carpio, L.L. Bonilla, Pulse propagation in discrete systems of coupled excitable cells, SIAM J. Appl. Math. 63 (2) (2002) 619–635.
 T. Erneux, G. Nicolis, Propagating waves in discrete reaction-diffusion systems, Physica D 67 (1993) 237–244.
 X. Chen, S.P. Hastings, Pulse waves for a semi-discrete Morris-Lecar type model, J. Math. Biol. 38 (1999) 1–20.
 G. F´ath, Propagation failure of traveling waves in a discrete bistable medium, Physica D 116 (1998) 176–180.
 R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1 (1961) 445–466; J. Nagumo, S. Arimoto, S. Yoshizawa, An active impulse transmission line simulating nerve axon, Proc. Inst. Radio Engineers 50 (1962) 2061–2070.
 J. Grasman, Asymptotic methods for relaxation oscillations and applications, Applied Mathematical Sciences, vol. 63, Springer, New York, 1987.
 J.P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987) 556–572.
 J.P. Keener, Waves in excitable media, SIAM J. Appl. Math. 39 (1980) 528.
 Y. Kuramoto, T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Prog. Theor. Phys. 55 (1976) 356–369.
 P.A. Lagerstrom, Matched Asymptotic Expansions, Springer, NY, 1988.
 K. Maginu, Stability of periodic traveling wave solutions with large spatial periods in reaction-diffusion systems, J. Diff. Eqs 39 (1981) 73–99.
 K. Maginu, Stability of spatially homogeneous periodic solutions of reaction-diffusion equations, J. Diff. Eqs 31 (1979) 130–138.
 J. Mallet-Paret, The global structure of traveling waves in spatially discrete dynamical systems, J. Dynam. Diff. Eqs. 11 (1999) 1–47.
 C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle-fiber, Biophys. J. 35 (1981) 193–213.
 J.C. Neu, Chemical waves and the diffusive coupling of limit oscillators, SIAM J. Appl. Math. 36 (1979) 509–515.
 J.C. Neu, Large populations of coupled chemical oscillators, SIAM J. Appl. Math. 38 (1980) 305–316.
 S. Binczak, J.C. Eilbeck, A.C. Scott, Ephaptic coupling of myelinated nerve fibers, Physica D 148 (2001) 159–174.
 A. Tonnelier, McKean caricature of the FitzHugh-Nagumo model: Traveling pulses in a discrete diffusive medium, Phys. Rev. E 67 (2003) 036105.
 B. Zinner, Existence of traveling wave front solutions for the discrete Nagumo equation, J. Diff. Eqs. 96 (1992) 1–27.
|Deposited On:||24 Apr 2012 09:06|
|Last Modified:||06 Feb 2014 10:13|
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