一维4次方映射系统参数空间解域研究

Investigation of the Topology of the Codimention Space of a Quartic Map

利用同周期图方法,从不同的初始点出发研究了一维双参数4次方映射系统的参数空间解域结构。结果表明:该映射系统参数空间存在大量无穷自相似的"小虾"状精细结构,并按照一定的规律排列在"混沌海"中。与单参数系统不同,双参数系统参数空间存在多吸引子共存区域,这些特殊区域的解域结构敏感地依赖于初始点。

By the method of Iso-periodic diagrams, this paper investigates the topology of the codimention space of the dynamical system： A kind of quartic map. The codimention space is reported to be organized in a simple way： it consists of a “structures-parallel-to-structures” sequence of shrimp-shaped islands immersed on a via caotica. These shrimp-shaped islands organize in a regular way along a special direction. Being different from the single codimention system, these two codimention systems contain multiple attractors＇ domain and the Topology of these domains are sensitively depended on the initial conditions.