Bifurcations in a discrete nonlinear diffusion equation
Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 689-697
Yong-In Kim
University of Ulsan
Abstract : We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery states of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficient of the linear part of the given nonlinearity.
Keywords : bifurcation, diffusion equation
MSC numbers : 34C, 58F
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