Title: LogisticMap Post by: FuKwun Hwang on June 13, 2010, 02:13:14 pm The logistic map
The logistic equation was first proposed by Robert May as a simple model of population dynamics. This equation can be written as a onedimensional difference equation that transforms the population in one generation, x_{n}, into a succeeding generation, x_{n+1}. x_{n+1} = 4 r x_{n} (1x_{n}) Because the population is scaled so that the maximum value is one, the domain of x falls on the interval [0; 1]. The behavior of the logistic equation depends on the value of the growth parameter, r. If the growth parameter is less than a critical value r<0.75.., then x approaches a stable fixed value. Above this value for r, the behavior of x begins to change. First the population begins to oscillate between two values. If r increases further, then x oscillates between four values. Then eight values. This doubling ends when r > 0.8924864... after which almost any x value is possible. Author : Francisco Esquembre and Wolfgang Christian. Text and original idea from the Open Source Physics project manual Date : July 2003 Title: Re: LogisticMap Post by: Mansadi on December 11, 2019, 10:22:23 am I know it's too hard to understand. But the knowledge in the body.
