Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 35 Issue 4
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- Pages.689-700
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- 1998
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
BIFURCATIONS IN A DISCRETE NONLINEAR DIFFUSION EQUATION
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 state 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 coefficients of the linear part of the given nonlinearity.