Talk:Logistic function

message: INCORRECT LINK
I believe the "Supremum" link is misassociated.  It goes to "Infimum" instead of "Supremum".  — Preceding unsigned comment added by 67.42.51.73 (talk) 21:14, 21 January 2023 (UTC)
replies: text: The "Supremum" link is correctly linked to the page Supremum, which is redirected to the page Infimum and supremum. — Andy Anderson 22:48, 21 January 2023 (UTC)
replies: text: I meant ... the "hover" link goes to Infimum rather than Supremum.  Don't know if that is improvable or not. 67.42.51.73 (talk) 03:06, 22 January 2023 (UTC)
replies: text: Default Wikipedia behavior, unfortunately. The hover displays the first paragraph of the linked page, and the supremum description is in the second paragraph. I merged the two paragraphs, and now at least part of the description shows up. — Andy Anderson 04:20, 22 January 2023 (UTC)

message: I am having some problems w/ getting this correct, and it is very clear it has been three decades since I took calculus!
* NOTE: Notation variation is common in this ubiquitous function, particular as it defines a wide range of natural system behavior over time.
** Logistic growth (where this is the model of a population size), one of the most commmon applications of this function, is a function of time, so other sources may use t as the variable, and x to represent the population size.  Also, some sources represent the population size (i.e. the y value) using pₜ (to incidate popuation of p at time t, with p₀ representing the initial population, i.e. at t₀
** Logistic growth, when it is represented as a function of time, often will N,N_t, P, or P'_t to reprsent the y value.
** Other sources using other constants, e.g. both  K and M are used fairly frequently for the carrying capacity (maximum population size a system can support).
** Finally, the coeficient of the exponent also is frequently represented with r, and much less often, with μ, rather than k.
*So the above can be seen as:
  N_{t}  = \frac {K N_0 }  {N_0+({K-N_0})e^{-rt} } 
which (well, should be) is the same as
 N_{t} = \frac {K N_0 e^{rt}} {({K-N_0}) + {N_0 e^{rt}}} 
and
*Where:
**Nₜ is the population at time = t
**K is the Carying capacity 
**r (the variable name used by Fisher in The Genetical Theory of Natural Selection) is the Population growth rate 
**t is time (note: must be of same magnitude/units as in r)
Some authors disregard convention and stick to x and y with a,b, and c as various constants.
=== Question: Should we add discussion about what happens w/ r>3???===
The behavior of logistic growth, the stable basis of how most everything in the Universe seems to function, becomes rather interestng as r hits about 3, as seen on every article written about the Logicistic map showing its Bifurcation diagram.
We go from a very simple curve that underlies all living systems at multiple levels of emergence, radioactive decay, chemical kinetics, the spread of conspiracy theories, etc. to a great example of chaos theory. Initially, you see behavior that looks exactly like what we see in nature:  a bit of an overshoot of K, with some ocilations around N=K until it settles down after a few periods.  Crank it up a bit more and you start making fractals.  The solution for this complex/chaotic behavior from a simple function is non-trivial and  probably deserves some discussion by someone who is a bit fresher on the math
Its very telling, and worth discussion, that such a fundamental, and simple, eqution which underpins much of our experienced University resuts in  chaos and while I don't want to introduce anything about butterfly wings in this dicussion, the impact of this behavior is real and inevitable.  
DrKC MD (talk) 04:11, 2 February 2024 (UTC)
thread_title:  Notionational differences and different forms

message: The behavior of logistic growth, the stable basis of how most everything in the Universe seems to function, becomes rather interestng as r hits about 3, as seen on every article written about the Logicistic map showing its Bifurcation diagram.
We go from a very simple curve that underlies all living systems at multiple levels of emergence, radioactive decay, chemical kinetics, the spread of conspiracy theories, etc. to a great example of chaos theory. Initially, you see behavior that looks exactly like what we see in nature:  a bit of an overshoot of K, with some ocilations around N=K until it settles down after a few periods.  Crank it up a bit more and you start making fractals.  The solution for this complex/chaotic behavior from a simple function is non-trivial and  probably deserves some discussion by someone who is a bit fresher on the math
Its very telling, and worth discussion, that such a fundamental, and simple, eqution which underpins much of our experienced University resuts in  chaos and while I don't want to introduce anything about butterfly wings in this dicussion, the impact of this behavior is real and inevitable.  
DrKC MD (talk) 04:11, 2 February 2024 (UTC)
thread_title:  Question: Should we add discussion about what happens w/ ''r''>3???

message: I have to edit / make a wiki page for a project. I proposed to make a page titled Logistic Equation
The page will basically link to here if people are looking for it continuous version (Logistic Differential Equation)
and to the logistic map page if people are looking for its discrete form. Unless of course there are major objections from people. 
I feel the Logistic Equation is worthy of a page on its own as if you type logistic equation in google
the mathworld page comes up first on the search.   —Preceding unsigned comment added by Rjor2 (talk • contribs) 12:51, 19 February 2010 (UTC)
thread_title:  Logistic Equation Page 

message: The next major task is to present the simple differential equation into the wider mathematical context. In other words, from this starting point we ought to generalize and make connection with the original of Pierre François Verhulst.
This is the task scheduled for today.--Михал Орела (talk) 08:14, 19 October 2008 (UTC)
thread_title:  Logistic differential equation 

message: can we please have instructions for how to fit a logistic curve's parameters to data?   Is there an analytic way to do this; or do you just have to use numerical methods like gradient descent and pray that it converges?
:The Levenberg-Marquardt algorithm is a very general method that may be applicable here, depending on what exactly it is that you want to do. --MarkSweep (call me collect) 08:50, 22 March 2006 (UTC)
thread_title: request

message: The plot needs labels on the X and Y axis!
Targa86 21:25, 28 June 2007 (UTC)
thread_title: Plot

message: The three pages sigmoid, sigmoid function, and logistic curve seemed rather confusing for readers. So I have moved all info on the "standard" logistic curve 1/(1+exp(-t)) to sigmoid function, and kept here only the stuff about more general logistic curves that are shifted and scaled copied of the latter. I have provided a general formula for these curves, but I am not familiar with this field so I do not know whether the formula and parameters that I picked are OK.  If there is a "canonical" formula, would someone please provide it?Also the plot shows the standard sigmoid function; here one should have a plot of the more general logistic curve, shifted and scaled.Jorge Stolfi 07:37, 2 Jul 2004 (UTC)
thread_title: Standard formula needed

message: Argh.. I moved logistic curve to logistic function because it seemed more logical, but now I see that most users call it "curve".  Profuse apologies.  If you can, could you please reverse the move, making logistic function into a redirect?  Thanks...Jorge Stolfi 08:01, 2 Jul 2004 (UTC)
thread_title: Logistic curve vs. logistic function

message: The phrasing and structure of the article mistakes the logistic function for one of its applications, namely modeling population growth.  Instead, the logistic function should be introduced as a mathematical function.  It surely it has mathematical properties.  Other important applications are found, for example, in machine learning and statistics. -Pgan002 21:47, 7 February 2006 (UTC)
thread_title:  Article has wrong focus 

message: I came across this curve while examining the qustion: what does it mean to double a probability? Eventually I decided that a nice way to do it is to duble the ratio r = p/(1-p). In effect, this treats the probability as being expressed as gambling odds.
If you take the log of this value ln(p/(1-p)) and flip the x any y axes y=exp(x)/exp(x+1) you get the logistical curve.
Pmurray bigpond.com 06:08, 5 June 2006 (UTC)
thread_title:  Another pov 

message: The page on logit and logistic function appear to regard the exact same topic, the logistic function. As such, I propose that they be merged. The primary portion of the logit page that I think bears inclusion in this page is the comment at the top regarding logistic regression (in italics). Pdbailey 17:11, 13 June 2007 (UTC)
replies: text: I am not against a merge, but let's note they are different topics, albeit each other's inverse.  Logit would need its own section which would be a redirect target, right?  Now that the logit page is cleaned up, it may be doable.  Baccyak4H (Yak!) 17:37, 13 June 2007 (UTC)
replies: text: The more I thought about it, these two articles focus quite clearly on the two functions and little ink (pixels?) would be spared merging. The fact that one is the others inverse doesn't appear to be relevant to either article's point. Pdbailey 23:45, 13 June 2007 (UTC)
thread_title:  proposed merge with logit 

message: The section on history suggests that equation 1 was first proposed by... but there is no equation 1. I'd link it if I knew which one it was. Pdbailey 17:09, 13 June 2007 (UTC)
thread_title:  no equation 1 

message: The first image on the page, the plot of the logistic function, appears to be broken to me.  Anyone else having this problem?
128.97.68.15 (talk) 17:18, 30 October 2008 (UTC)
replies: text: At first glance it looks OK to me - a red S-shaped curve passing through (0, 0.5) with asymptotes y=0 and y=1. I'm using IE6. What do you see?--A bit iffy (talk) 17:26, 30 October 2008 (UTC)

text: It looks fine on Firefox and Safari; I will check with Opera now. --Михал Орела (talk) 09:08, 31 October 2008 (UTC)

text: Just checked with Opera browser; everything is "beautiful" --Михал Орела (talk) 09:16, 31 October 2008 (UTC)
thread_title:  image problem 

message: Can we say more about the solution to the logistic differential equation than to use Mathematica? The equation is a lovely example of a Bernoulli differential equation, and mentioning the fact gives an easy explicit solution given an initial value. No need to mask pretty mathematics.
--Moly 04:24, 21 January 2009 (UTC)
replies: text: Looked at the Bernoulli differential equation you mentioned! It is very raw Mathematics :-) In other words there is very little "English text" to suggest to the "uninitiated" where the equation comes from and why it is significant. Perhaps you might elaborate on its "beauty" there and then see how to fit the logistic differential equation example into place?--Михал Орела (talk) 14:17, 27 January 2009 (UTC)
thread_title:  Solution of the Logistic Differential Equation 

message: I am looking at the following section:
"Logistic functions are often used in neural networks to introduce nonlinearity in the model and/or to clamp signals to within a specified range. A popular neural net element computes a linear combination of its input signals, and applies a bounded logistic function to the result; this model can be seen as a "smoothed" variant of the classical threshold neuron.
A reason for its popularity in neural networks is because the logistic function satisfies the differential equation
:y' = y(1-y).\,
The right hand side is a low-degree polynomial. Furthermore, the polynomial has factors y and 1 − y, both of which are simple to compute. Given y = sig(t) at a particular t, the derivative of the logistic function at that t can be obtained by multiplying the two factors together. These relationships result in simplified implementations of artificial neural networks with artificial neurons."
There are no citations to support the assertions in the text. I will look into remedying this now. In addition, to argue the case that it is popular in neural networks precisely because it satisfies  the given differential equation is not a good argument, in my opinion. I will replace this with specific examples from the neural network literature (and thus "prove" the assertion by example :) )--Михал Орела (talk) 16:46, 29 January 2009 (UTC)
replies: text: g(h) = \frac{1}{1 + e^{-2 \beta h}} \! 
which we recognize to be of the form of the logistic function.
The text is taken from Gershenfeld 1999, p.150--Михал Орела (talk) 19:05, 29 January 2009 (UTC)
thread_title:  Neural Networks 

message: The origin of the term "logistic" is obscure. This word is far from self-explanatory. Thus, unlike for most other scientific terms, trying to look at its latin/greek etymology (e.g. consulting wiktionary) provides no insight really to the meaning of the concept. Could someone throw some light on the logic (if any) behind the word "logistic", especially when used in the present context? Typofier 22:34, 13 February 2009 (UTC)
thread_title:  Why is it called "logistic"? 

message: I miss some information about this... --Andrestand (talk) 10:26, 24 August 2009 (UTC)
replies: text: So the recurrence version is chaotic, the continuous version is not chaotic? --Alex1011 (talk) 10:18, 12 May 2012 (UTC)
thread_title:  Logistic function and chaos. 

message: Using the right variables, the population function can help you determine how long it takes to heal a broken heart:
: t = \frac{.02 e^{.1x}}{2 + .01 \left( e^{.1x} - 1\right)} 
where x is the time you were with someone in months, and t is the expected grieving time in months.  Alternately, you might try seeing a counselor.
Loosenut (talk) 04:41, 23 March 2010 (UTC)
thread_title:  Logistic function and heartbreak 

message: Besides autocatalytic, two other items that are related: 1) (pH) titration curves, and 2) Avrami equation for crystallization. Dagordon01 (talk) 01:38, 6 June 2011 (UTC)
thread_title:  Expand chemistry 

message: What is "d"? How am I supposed to find out? If you assume the reader already knows, what is the purpose of Wikipedia? DEFINE TERMS. PROVIDE LINKS. TEACH. Thanks.  — Preceding unsigned comment added by 70.41.216.250 (talk) 19:43, 12 March 2012 (UTC)
replies: text: In:        \frac{d}{dt}P(t) , 
\frac{d}{dt} is a differential operator.  It is calling for the derivative of P(t) with respect to t.Phmoreno (talk) 23:49, 12 March 2012 (UTC)
thread_title:  If you present a formula, define it's terms. All of them. 

message: I'm really a layman but i can't help but notice similarities to the error function, could someone explain whether and if so what the similarities are between this two? thanks in advance
Andy Jiang (talk) 05:27, 17 May 2012 (UTC)
thread_title:  relating similarities to the error function 

message: In the beginning of the article, one reads: The logistic function is the sigmoid curve with equation: f(x) = \frac{1}{1 + \mathrm e^{-x}} . But later on, the plural logistic functions is also used. Is there one logistic function or are there many? Jaan Vajakas (talk) 14:55, 9 February 2014 (UTC)
thread_title:  Is there one logistic function or many? 

message: Currently, the intro of this page reads "A logistic function or logistic curve is a common special case of the more general sigmoid function," and the intro to the sigmoid function on its page reads "Often, sigmoid function refers to the special case of the logistic function." They cannot be special cases of each other. Also, they are both defined exactly the same, which doesn't make sense. If that is true, then they are equivalent and I would think the two pages should be merged or link to each other. Is it correct that the sigmoid function is a special case of the "logistic curve"? 2001:4898:80E0:EE43:0:0:0:3 (talk) 18:41, 7 August 2014 (UTC)
thread_title:  Congruency between Sigmoid Function and Logistic Function 

message: I'm not very proficient in editing wikipedia, so hopefully someone else can look into this and figure out the right course of action. In "See Also", there is a link to "Constructal Law" which I believe bears little relation to the topic of this page. The link was put there by a user "Mre env" (http://en.wikipedia.org/wiki/User:Mre_env) whose edit history seems to be entirely based upon spreading links and references to this supposed law around the wiki. I've undone two of his recent edits, which even plagiarized the source he was citing, but I imagine there are better ways to handle this, since it seems to be continuous and pervasive. 38.65.195.5 (talk) 00:07, 19 February 2014 (UTC)
replies: text: I've made a notice on Wikipedia:Fringe theories/Noticeboard, so hopefully this will get figured out. 38.65.195.5 (talk) 00:58, 19 February 2014 (UTC)

text: It seems to be a small consensus that it is a WP:FRINGE topic, and it is also referenced in the section "In design in nature: spreading and collecting flows". I'm removing both the link and that section. 38.65.195.5 (talk) 18:28, 19 February 2014 (UTC)
thread_title:  Constructal theory link 

message: According to the first sentence in the article, it is a logistic function, indicating that there is a family of logistic functions. At the same time, it defines such a function as
:f(x) = \frac{1}{1 + \mathrm e^{-x}},
indicating that there is only one such function. So, is there many logistic functions or only one? —Kri (talk) 20:43, 22 October 2014 (UTC)
replies: text: If one reads the article carefully, the function you mention above is a standard logistic function. The usual parameterized version of the logistic function is noted in the lead. Also there is no mention of a family of logistic functions; rather it is a logistic family of distributions, which is a different thing. I have also seen mentioned a family of logistic functions, in the context of iterated functions and period doubling in the logistic map. --Mark viking (talk) 19:12, 8 April 2016 (UTC)
thread_title:  Is it ''a'' logistic function or ''the'' logistic function? 

message: In the section "Logistic differential equation", we have three ways of expressing zero: "0", "zero" and "null"; and two ways of expressing one: "1" and (strangely) "unit".  I'm going to simplify these to use the figures "0" and "1", or the words "zero" and "one", as appropriate.
yoyo (talk) 16:15, 9 October 2017 (UTC)
replies: text: Done.  Turns out it was clearer to use the figures "0" and "1" rather than the words "zero" and "one" in those places.  yoyo (talk) 16:25, 9 October 2017 (UTC)
thread_title:  Logistic differential equation - simpler language 

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thread_title:  External links modified