Stability of a Certain 2-Dimensional Map with Cobweb Diagram

摘要

In this paper, we investigate the following discrete-time map: x_(n+1) = Φ(y_n), y_(n+1) = ψ(x_n). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.