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I am wondering (and searching with no success) if there are any examples of differential equations in psychology?

I mean, no tutorial explaining what is differenetial equations or even partial differential equations, but a research (like in emotions or social psychology, or cognitive psychology) by psychologists that use these equations to model the data?

[update, 29.05.2016] Stack Community always reminds me that the quality of the answers depends on the question asked. Just as a good question is half of the problem.
I'll try to make myself clear with an example. I thought about an article in psychology, say about cognitive dissonance, emotions, coping or else, that use differential equations to decribe phenomenon without invoking physics or chemistry or other hard science. Article by Deboeck & Bergeman introduces pendulum model(Christiaan's comment). But I don't have to refer to physics when doing ordinary squares regression, so that's why I thought it is possible to use differential equations without explicite references to physical models.

June 2, 2016: I never suggested we could "use differential equations without explicit reference to physical models". I have always said the same: the mathematical interpretation of cellular processes has lost prominence (owing to further research). The biological processes obviously remain; the interpretation has not been able to hold. Teresa Pelka

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    $\begingroup$ a google search yields quite a bunch of hits - first hit (on my pc that is): ncbi.nlm.nih.gov/pubmed/23527605 - search terms - your title :-) 'differential equations in psychology' $\endgroup$
    – AliceD
    May 23, 2016 at 8:42
  • $\begingroup$ @Christiaan as far as I know Internet browsers can provide divergent search answers based on your previous activity, which is unique. But as I said I did my own search and research and found this article before heading to Stack. $\endgroup$ May 29, 2016 at 9:40
  • $\begingroup$ @huh I think you should post that as an answer. $\endgroup$ Jun 2, 2016 at 8:46
  • $\begingroup$ You can have a look at this recent model: ncbi.nlm.nih.gov/pmc/articles/PMC9945965 $\endgroup$
    – Dadep
    May 4, 2023 at 14:49

2 Answers 2

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The Hodgkin and Huxley model of neuronal firing is based on non-linear differential equations. A significant portion of research on sensation and perception is based on such models.

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A large and notable area within psychology to which differential equations are central is dynamical systems theory. It is widely applied to cognitive science. Differential equations are used to describe (model) the states on one or more dimensions that a system can take which changes over time. Dynamical systems have been widely used to model cognition.

Many applications of dynamical systems theory in psychology accordingly concern questions classically within the scope of cognitive psychology, but there are examples from other areas like social and developmental psychology.

Mind that dynamical systems theory originated within physics, specifically mechanics, and that accordingly it has been widely used to model material processes. However the use of models from physics is not uncommon in psychology (think of conceiving the circadian rhythm as a harmonic oscillator (pendulum) or Lorenz' psychohydraulic model of motivation) and the states of some modelled system can be highly abstract and ›non-physical‹.

Since dynamical systems have been discussed here to some extent, I am referring you to this and this question instead of providing more information here.

Let me however second the recommendation of Schöner's »Dynamical Systems Approaches to Cognition« in Sun (ed.): Cambridge Handbook of Computational Psychology (2008) there for a decent overview, and point out a passage on nonlinear dynamical system modeling in R.W.J. Neufeld's chapter »Mathematical and Computational Modeling in Clinical Psychology« in Busemeyer et al. (eds.): The Oxford Handbook of Computational and Mathematical Psychology (2015).

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