带有同号截距和负斜率的一维不连续分段线性映射的边界碰撞分叉曲线  

Border Collision Bifurcation Curves in 1D PWL Discontinuous Maps with the Same Intercept Sign and Negative Slope

作　　者：顾恩国[1] 卢俊波 罗阿木 刘阳庆 GU Enguo;LU Junbo;LUO Amu;LIU Yangqing(College of Mathematics and Statistics, South- Central University for Nationalities, Wuhan ~3007~, Chin)

机构地区：[1]中南民族大学数学与统计学学院,湖北武汉430074

出　　处：《应用数学》2018年第2期350-356,共7页Mathematica Applicata

基　　金：国家自然科学基金资助项目(61374085)

摘　　要：本文研究一维带有同号截距的分段线性映射动力系统的边界碰撞分叉问题.根据截距的位置关系,将问题分成两类,并采用Leonov方法来研究边界碰撞分叉曲线.另外确定了边界碰撞分叉曲线和flip分叉曲线所围成的周期区域.研究结果表明,当分段线性映射具有同号截距时,其具有非常丰富的周期结构.This article aims at searching for the border collision bifurcation curves in 1D piecewiselinear maps with the same intercept sign. According to the location of two intercepts, we classify the problem into two cases. Then we use Leonov approach to analyze border collision bifurcation curves. We also present the periodic region that formed by border collision bifurcation curves and flip bifurcation curve. The result has shown that when the 1D piecewise-linear maps have the same intercept sign, it has a rich periodic structure.

关 键 词：分段线性映射 边界碰撞分叉曲线 周期递增结构 

分 类 号：O19[理学—数学]