Affiliation:
1. Department of Physics, Waseda University , Shinjuku, Tokyo 169-8555, Japan
Abstract
The stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation parameter in the discrete dynamical systems, and the emergence condition of an additional bifurcation, flip bifurcation, is identified. The correspondence between the discrete dynamical systems with positivity and the ultradiscrete ones derived from them is discussed. It is found that the derived ultradiscrete max-plus dynamical systems can retain the bifurcations of the original continuous ones via tropical discretization and ultradiscretization.
Funder
Japan Society for the Promotion of Science
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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