| 摘要: |
| 针对一类生物种群总量变化模型fλ(x)=λsinπx，提出了该模型中不同λ值下的动力性分析；该方法对λ的取值区间进行分类，分别通过两种方法分析其动力性，与传统方法相比，更容易被应用于不同的模型中；该研究结合离散动力系统，不变集，斥子和Hausdorff测度的定义和性质，将Lagrange中值定理应用到该模型逆映射的两个不同分支中，得到了有关fλ的逆映射的不等式，进而得到fλ存在唯一不变集的条件和不变集与斥子间的关系;最后，对较大的系数λ，估计了fλ(x)的斥子的Hausdorff维数；对于区间(0,1］上的系数λ，分别研究了fλ(x)迭代的动力性, 研究结论比传统方法更容易应用于相应的生物种群模型。 |
| 关键词: 动力系统 不动点 不变集 吸引子 斥子 Hausdorff维数 |
| DOI： |
| 分类号: |
| 基金项目: |
|
| The Study on Dynamics of a Class of Biological Population Model |
|
DENG Di, CHEN Zhen,HUANG Hua-ying
|
| Abstract: |
| For a total change model of a class of biological population: fλ(x)=λsinπx, dynamic analysis of different λvalue in the model is proposed. Firstly, the method classifies the range of λ, then the dynamical properties of fλ(x)are analyzed from two points. Compared with traditional methods, it is more easily applied to different models. Lagrange Mean Value Theorem is applied to the two different branches of the inverse mapping of the model, and the inequality of the inverse mapping about fλis obtained by combining the definitions and properties of the discrete dynamical system, invariant set, repellers and Hausdorff dimension. Then the condition of existence of a unique invariant set and the relationship between the invariant set and the repellers are obtained. Finally, for a larger coefficient λ, the Hausdorff dimension of fλ(x) repellers is estimated. For the coefficientλon interval(0,1］, the dynamical properties of fλ(x)iteration are studied respectively. The conclusion of the study is more likely to be applied to the corresponding biological population model than the traditional method. |
| Key words: dynamic system fixed point invariant set attractor repellors Hausdorff dimension |
