On the creation of Wada basins in interval maps through fixed point tangent bifurcation

Basin boundaries play an important role in the study of dynamics of nonlinear models in a variety of disciplines such as biology, chemistry, economics, engineering, and physics. One of the goals of nonlinear dynamics is to determine the global structure of the system such as boundaries of basins. A basin having the strange property that every point which is on the boundary of that basin is on the boundary of at least three different basins, is called a Wada basin, and its boundary is called a Wada basin boundary. Here we consider maps on the interval. We present a sufficient and necessary condition guaranteeing that three Wada basins are emerging from a tangent bifurcation for certain one-dimensional maps having negative Schwarzian derivative, two fixed point attractors on one side of the tangent bifurcation, and three fixed point attractors on the other side of the tangent bifurcation. All the conditions involved are numerically verifiable. (c) 2005 Elsevier B.V. All rights reserved.