二维含参映射系统分叉曲线的数值计算

NUMERICAL CALCULATION OF THE BIFURCATION CURVES OF PARAMETRIZED TWO-DIMENSIONAL MAPS

A numerical method has been proposed to calculate the bifurcation curves of parametrized two-dimensional maps. Under the weakest definition of bifurcation (branching.), this method is a direct extension of the idea suggested by one of the authors to general two-dimensional parametrized maps. The recursion formulas required in the calculation have been given. Moreover, the structure of k-period solution on both sides of the bifurcation carves been been discussed from the viewpoint of stability. According to some further definitions of bifurcation, we suggested, a way to determine the bifurcation curves under respective criteria numerically. Two examples of the Henon map and a coupled logistic map have beea treated and some new results'have been obtained.