A simple population model with qualitatively uncertain dynamics
Basins of attraction of nonlinear systems can be "riddled"; arbitrarily close to any point in a riddled basin are neighboring points which go to a different attractor. I present two chaotically forced single-species population models with riddled basins of attraction. As a result of this complex basin structure, the ultimate survival of these populations is effectively unpredictable. Riddled basins produce a level of unpredictability qualitatively greater than the familiar sensitive dependence on initial conditions within a single chaotic attractor, or the unpredictability caused by multiple attractors with fractal basin boundaries.Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited
Neubert
MG
Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, U.S.A.