种群方程Nt+1=λNtexp（-aNt）中的Feigenbaum现象

THE FEIGENBAUM’ S PHENOMENON IN THE EQUATION DESCRIBING THE GROWTH OF BIOLOGICAL POPULATIONS

一、引言现代科学技术的发展,打破了传统学科的界限。近年来,在研究非线性系统的奇异现象——分枝、浑沌、奇异吸引子等问题时,科学家们从各自不同的领域走到一起来了。气象学家研究大气动力学中的非线性微分方程,物理学家研究流体湍流、激光、行星轨道、闪烁的氖管、回旋中子星、化学家在研究物理化学、化学湍流,经济学家研究货币在时空中不规则流通。

This paper discusses the complicated dynamical behavior of the simplest nonlinear difference equation N（?）+1=λN1exp （-aN1） which describes the growth of biological populations. For the different values of the parameter X the global structure of orbits of the equation is analysed. More values of the bifurcation of the equation than those given in R. M. May’ s work’ s are computed and therefore the Feigenbaum’ s phenomenon in the successive bifurcation process are found. The Feigenbaum’ s constant δ≈4. 669.