| 一类具有食物偏好的三种群生物模型的动力学分析 |
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| 引用本文： | 周伟,;饶晓波,;王晓雪. 一类具有食物偏好的三种群生物模型的动力学分析[J]. 兰州交通大学学报, 2014, 0(3): 46-53 |
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| 作者姓名： | 周伟, 饶晓波, 王晓雪 |
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| 作者单位： | [1]兰州交通大学数理学院,甘肃兰州730070; [2]兰州交通大学附属小学,甘肃兰州730070 |
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| 摘 要： | 利用Kolmogorov定理和Lyapunov稳定性定理对一种带有食物偏好的生物种群模型的稳定性进行了分析,得到了平衡点和极限环稳定的充分条件.而后利用分岔图、Poincaré映射图及相图等数值方法研究了系统复杂的动力学行为,发现了系统经由两种非常规周期倍化分岔——"混沌泡"和"周期泡",进入混沌的道路.最后,利用Floquet理论数值验证了系统的倍周期分岔行为.
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| 关 键 词： | 倍周期分岔 混沌 Floquet特征乘子 Kolmogorov 定理 |
Dynamical Analysis of a Three-Species Biological Model with Food Preferences |
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| Affiliation: | ZHOU Wei, RAO Xiao-bo, WANG Xiao-xue (1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China; 2. The Primary School Affiliated to Lanzhou Jiaotong University, Lanzhou 730070,China) |
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| Abstract: | The stability of a biological population model with food preferences is analyzed based on Kolmogorov theorem and Lyapunov stability theorem.The sufficient conditions of stable equilibrium points and limit cycles for the model are obtained,respectively.Then the complex dynamical behaviors of this system are studied by bifurcation diagram,Poincar＆#233;sections and phase portraits, and two irregular routes to chaos through period-doubling bifurcation are found by numerical methods,which are＆quot;chaotic bubble＆quot;and＆quot;cycle bubble＆quot;.Finally,the behavior of period-doubling bifurcation is proved numerically by using Floquet multipliers. |
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| Keywords: | period-doubling bifurcation chaos Floquet multiplier Kolmogorov theorem |
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