Sánchez-Garduño, F. and Maini, P. K. (1997) Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations. Journal of Mathematical Biology, 35 (6). pp. 713-728.
In this paper we study the existence of one-dimensional travelling wave solutions for the non-linear degenerate (at u=0) reaction-diffusion equation where g is a generalisation of the Nagumo equation arising in nerve conduction theory, as well as describing the Allee effect. We use a dynamical systems approach to prove: 1. the global bifurcation of a heteroclinic cycle (two monotone stationary front solutions), for c=0,2. The existence of a unique value of c for which is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts for . We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation.
|Uncontrolled Keywords:||Sharp fronts · Degenerate diffusion · Hamiltonian · Bifurcation of heteroclinic trajectories|
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||06 Dec 2006|
|Last Modified:||20 Jul 2009 14:21|
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