- #1

fog37

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- TL;DR Summary
- Recursive equations as composite equations

Hello,

I am trying to better understand the following discrete, recursive equation (logistic equation):

$$x_{n+1} =r x_n (1- x_n)$$

Is this an equation with two variables, ##x## and ##t##, where ##t## assumes discrete values, or is it an equation with one single variable, the variable ##x##? Is it a composite function?

If ##n## is the time integer variable, then the value of the variable ##x## at time ##n \Delta t ## seconds depends on the value of ##x## at time ##(n-1) \Delta t##. Time is discrete and changes by ##\Delta t##.

If time was not discrete but continuous, how would the equation look like? Would it be ##x(t)= r x(t-1) [1-x(t-1)]##? I don't think so...

thanks!

I am trying to better understand the following discrete, recursive equation (logistic equation):

$$x_{n+1} =r x_n (1- x_n)$$

Is this an equation with two variables, ##x## and ##t##, where ##t## assumes discrete values, or is it an equation with one single variable, the variable ##x##? Is it a composite function?

If ##n## is the time integer variable, then the value of the variable ##x## at time ##n \Delta t ## seconds depends on the value of ##x## at time ##(n-1) \Delta t##. Time is discrete and changes by ##\Delta t##.

If time was not discrete but continuous, how would the equation look like? Would it be ##x(t)= r x(t-1) [1-x(t-1)]##? I don't think so...

thanks!

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