MHB Real life phenomenon that can be modeled by this curve?

[das1]

Is there any real life phenomenon that can be modeled by the curve:

S(t) = 1/(1+e^-t) ?

in the range between t=-5 and t=5

Thanks!

 

[stainburg]

Sigmoid function? Sigmoid function - Wikipedia, the free encyclopedia

 

[das1]

That's awesome, thank you!

How about the function y=1/x ?

Is there anything in reality that can be modeled by this function?

Thanks!

 

[stainburg]

That's awesome, thank you!

How about the function y=1/x ?

Is there anything in reality that can be modeled by this function?

Thanks!

Hilbert transform, which is quite useful for communication transmission. y=1/x is the convolution kernel. Hilbert transform - Wikipedia, the free encyclopedia

 

[Evgeny.Makarov]

How about the function y=1/x ?

Is there anything in reality that can be modeled by this function?

The electric potential of a point charge decreases as $1/x$ where $x$ is the distance.

 

[ThePerfectHacker]

Is there any real life phenomenon that can be modeled by the curve:

S(t) = 1/(1+e^-t) ?

in the range between t=-5 and t=5

Thanks!

Suppose $y(t)$ is the growth of a virus at time $t$. This quantity is usually modeled by the basic equation $y' = ay$ where $a$ is some positive constant.

However, this equation has limitation as it does not take growth constraints into account. A better equation for a population model that takes population limitations into account is to rather consider $y' = a(y) \cdot y$ where $a(y)$ depends on the quantity $y$, it gets smaller as $y$ gets larger. The simplest type of such a function is the linear function $a(y) = (b - cy)$ where $b,c$ are positive constants. Note that if $y$ is small then $b-cy \approx b$ and so we are back to the equation $y' = by$. However, the constant of growth gets smaller as $y$ increases.

This model $y' = (b-cy)y'$ of growth leads to the solution every similar to what you just posted.