Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems.

Abstract

Solution sensitivity to initial conditions in a first order delayed partial differential equation is investigated around the Hopf bifurcation and around higher order bifurcations. The presence of multistable limit cycles and the geometry of their basins of attraction are then investigated systematically for three different first order nonlinear ordinary differential delay equations.

Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems, R. Crabb, J. Losson, & M.C. Mackey. Proc. First Inter. Conf. Nonlin. Anal. (1996), 4, 3125-3136, de Gruyter, Berlin.