A global attractivity result for maps with invariant boxes
Date of Original Version
We present a global attractivity result for maps generated by systems of autonomous difference equations. It is assumed that the map of the system leaves invariant a box, is monotone in a coordinate-wise sense (but not necessarily monotone with respect to a standard cone), and satisfies certain algebraic condition. It is shown that there exists a unique equilibrium, and that it is a global attractor. As an application, it is shown that a discretized version of the Lotka-Volterra system of differential equations of order k has a global attractor in the positive orthant for certain range of parameters.
Discrete and Continuous Dynamical Systems - Series B
Kulenović, M. R.S., and Orlando Merino. "A global attractivity result for maps with invariant boxes." Discrete and Continuous Dynamical Systems - Series B 6, 1 (2006): 97-110. https://digitalcommons.uri.edu/math_facpubs/189