Properties of basins of attraction for planar discrete cooperative maps
Date of Original Version
It is shown that locally asymptotically stable equilibria of planar cooperative or competitive maps have basin of attraction B with relatively simple geometry: The boundary of each component of B consists of the union of two unordered curves, and the components of B are not comparable as sets. The boundary curves are Lipschitz if the map is of class C1. Further, if a periodic point is in @B, then @B is tangential to the line through the point with direction given by the eigenvector associated with the smaller characteristic value of the map at the point. Examples are given.
Discrete and Continuous Dynamical Systems - Series B
Kulenović, M. R.S., J. Marcotte, and O. Merino. "Properties of basins of attraction for planar discrete cooperative maps." Discrete and Continuous Dynamical Systems - Series B 26, 5 (2021): 2721-2737. doi:10.3934/dcdsb.2020202.