Applied Math Seminar: Nonlinear stability analyses of vegetative pattern formation in an arid environment
3:15 pm Neill 3W
David J. Wollkind
Abstract: The development of spontaneous stationary equilibrium vegetative patterns in an arid isotropic homogeneous environment is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a fourth-order partial differential time-evolution logistic equation for the total plant biomass per unit area divided by the carrying capacity of its territory and defined on an unbounded flat spatial domain. Those patterns which consist of parallel stripes, labyrinth-like mazes, rhombic arrays of rectangular patches, and hexagonal distributions of spots or gaps are generated by the balance between the effects of short-range facilitation and long-range competition. Then these theoretical predictions are compared with both relevant observational evidence and existing numerical simulations as well as placed in the context of the results from some recent nonlinear pattern formation studies.