The unique standard logistic function is the solution of the simple first-order non-linear ordinary differential equation = (()) with boundary condition = /. This equation is the continuous version of the logistic map.

In the logistic map, we have a function () = (), and we want to study what happens when we iterate the map many times. The map might fall into a fixed point, a fixed cycle, or chaos.

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive constant sometimes known as the "biotic potential" gives the so-called logistic map.

Mar 25, 2015 · The logistic function uses a differential equation that treats time as continuous. The logistic map instead uses a nonlinear difference equation to look at discrete time steps. It’s called the logistic map because it maps the population value at any time step to its value at the next time step: $latex x_{t+1} = r x_t (1-x_t)$

One can show there exist a unique symmetric quadratic-like F and linear function L which satisfy this equation. Then starting from any family of quadratic-like maps and picking the map in this family which is at the period-doubling limit, one can show that by repeatedly applying R to this map one gets closer and closer to F.

3 days ago · The model is continuous in time, but a modification of the continuous equation to a discrete quadratic recurrence equation known as the logistic map is also widely used. The continuous version of the logistic model is described by the differential equation.

This observation is not specific to the logistic map: any (discrete) dynamical system of a continuous function with period 3 also contains (unstable) points of every other integer period. This means that if period 3 is observed, one can find unstable trajectories of period 5, period 1, period 4952 and so on.

Oct 29, 2021 · In the idealized case of very long therapy, () can be modeled as a periodic function (of period ) or (in case of continuous infusion therapy) as a constant function, and one has that 1 T ∫ 0 T c ( t ) d t > r → lim t → + ∞ x ( t ) = 0 , {\displaystyle {\frac {1}{T}}\int _{0}^{T}c(t)\,dt>r\to \lim _{t\to +\infty }x(t)=0,}

In this paper we discuss an approach to discrete logistic growth that leads in a natural and accessible way to continuous logistic growth functions.

Sep 5, 2013 · how is the logistic function characterized by the differential equation df(x)/dx = f(x)(1-f(x)) the continuous version of the logistic map, given by the recursive function: x n+1 = x n (1-x n)?