Bulletin of the
Korean Mathematical Society BKMS

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