摘要
讨论了一般的广义Logistic映射:x’=rx(1-（x/K）<sup>θ</sup>（θ】0）.对系统不动点的稳定性进行了研究,指出了个系统是混沌的,接着讨论了具有随机扰动的广义Logistic映射logx<sub>n+1</sub>-logx<sub>n</sub>=a-bx<sub>n</sub><sup>θ</sup>+αε<sub>n</sub>（其中ε<sub>n</sub>为标准高斯白噪声）.特别对θ=2的广义Logistic映射在α充分小的情形下,讨论了映射的动力学性质,并且从理论上证明了当α→0时,具有随机扰动的广义Logistic映射logx<sub>n+1</sub>-logx<sub>n</sub>=a-bx<sub>n</sub><sup>θ</sup>+αε<sub>n</sub>趋于确定性的广义Logistic映射logx<sub>n+1</sub>-logx<sub>n</sub>=a-bx<sub>n</sub><sup>θ</sup>.
Based on the logistic map foundation, this article has discussed the stochastic perturbation generalized logistic map. Its model is:x'=rx(1-(x/K)~θ(θ>0) ,( ε_n is standard gauss white noise). First ,through the research to the fixed-point stability, we adapt the method of the numerical simulation, have pointed out this system is Chaos. Second ,when α is small enough, we have proved the stochastic perturbation generalized logistic map : logx_(n+1)-logx_n=a-bx_n~θ+αε_n is prone to deterministic generalized logistic map : logx_(n+1)-logx_n=a-bx_n~θ. Finally, when α is small enough, we have further discussed the properties of dynamics the generalized logistic map.
出处
《伊犁师范学院学报（自然科学版）》
2007年第2期1-4,共4页
Journal of Yili Normal University：Natural Science Edition
