Logistic Map 262 浏览 0关注

The logistic map is a polynomial map (mathematics)|mapping (equivalently, recurrence relation) of Quadratic function|degree 2, often cited as an archetypal example of how complex, chaos theory|chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, Baron May of Oxford|Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. Mathematically, the logistic map is written : (1)\qquad x_{n+1} = r x_n (1-x_n)where: :x_n is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0) :r is a positive number, and represents a combined rate for reproduction and starvation. This nonlinear difference equation is intended to capture two effects. * reproduction where the ...
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