二维Logistic映射中混沌与分形的研究

研究了二维Ｌｏｇｉｓｔｉｃ映射非线性动态行为的普适特征后发现，控制参数不同，二维Ｌｏｇｉｓｔｉｃ映射可分别按Ｆｅｉｇｅｎｂａｕｍ途径、Ｒｕｂｅｌｌｅ－Ｔａｋｅｎｓ－Ｎｅｗｈｏｕｓｅ方案和Ｐｏｍｅａｕ－Ｍａｎｎｅｖｉｌｌｅ途径走向混沌，且在控制参数空间中的较大区域，其通向混沌的道路与Ｈｏｐｆ分岔有关，在这些途径上可观察到锁相和准周期运动。同时对二维Ｌｏｇｉｓｔｉｃ映射的分形研究表明，控制参数不同，分

Researches on Chaos and Fractal of the Coupled Logistic Map

In this paper,we analyze some general features of the nonlinear dynamic activities of the Coupled Logistic Map.We find that,for the difference of the selected values of the three control parameters,chaotic patterns of the Coupled Logistic Map may emerge out of Feigenbaum route ,the Ruelle Takens Newhouse Scenario and Pomeau Manneville route respectively.However,there exist large regions of control parameter space where the approaches to chaos have something to do with Hope bifurcation and we can observe phase locking and quasiperiodic motion on these routes.At the same time, the researches on the fractal images of the Coupled Logistic Map make it clear that when the control parameters are different,the fractal images are different from each other and these fractal images exhibit the fractal property of self similarity.