Equivalent low-order model for a nonlinear diffusion equation

Abstract We present an equivalent low-order model for a simple PDE system that exhibits interesting low-dimensional dynamics with a rich variety of homoclinic phenomena and whose effective dimension may be gradually increased by means of system parameters. The system is a linear heat equation subject to a nonlinear and nonlocal boundary condition and the reduction procedure is based on a finite element method. We will show that both the PDE and ODE systems have indentical stationary solution with a very similar linear stability behaviour and exhibit also very similar dynamics, at least within parameter ranges corresponding to physical devices.