Chaotic Dynamics: Using College Students as Entities for Chaos Experiments

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    Chaotic Dynamics
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Discussion Overview

The discussion revolves around the feasibility of using a college student population as entities for experiments in chaotic dynamics. Participants explore the concept of modeling chaos through population dynamics and suggest various approaches for an undergraduate thesis on the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant proposes using the student population of a college department as a model for chaotic dynamics but seeks clarification on how to implement this.
  • Another participant emphasizes that a population must be engaged in specific activities to exhibit chaos, referencing population dynamics models that include variable breeding and death rates.
  • A suggestion is made to consider changes in student enrollment rates as a potential variable for modeling chaos.
  • Some participants recommend using established models, such as the Rössler attractor, and conducting a bifurcation study to analyze chaotic behavior.
  • There are inquiries about the necessity of software tools like Mathematica for conducting research on population dynamics and dynamical models.
  • Participants discuss methods for linearizing equations and computing eigenvalues to assess stability in chaotic systems.
  • Suggestions are made to explore numerical integration techniques, such as Euler or Runge-Kutta methods, for analyzing nonlinear equations and generating bifurcation diagrams.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of using a student population for chaos experiments, with some emphasizing the need for specific activities while others propose alternative modeling approaches. The discussion remains unresolved regarding the best method to pursue for the thesis.

Contextual Notes

Participants mention limitations related to the definition of chaos in population dynamics and the need for specific activities to model such dynamics effectively. There are also unresolved questions about the appropriate software tools and methods for analysis.

butoyzki
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i'm an undergraduate student decided to pursue a thesis on chaotic dynamics. would it be feasible to use the student population of my college department as an entity which will exhibit chaos? i need help, feel free to PM me or mail me: reysagana@gmail.com

thanks.
 
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You can't just use "a population" -- they have to be doing something!

Hence the field of population dynamics which generally uses toy-models which include changeable breeding and death rates to show the development of chaotic dynamics.
 
J77 said:
You can't just use "a population" -- they have to be doing something!

Hence the field of population dynamics which generally uses toy-models which include changeable breeding and death rates to show the development of chaotic dynamics.

how about the change in population of the students (e.g. the enrolment rate or the decrease/increase in enrolment)

would you suggest alternative subjects beside from the student population?
 
As it's an undergrad thesis, I'd advise you to take a well know model -- eg. http://en.wikipedia.org/wiki/Rössler_attractor -- and perform a bifurcation study; ie. with respect to showing you can do an analytical analysis, and write code to produce numerical bifurcation diagrams.
 
i have sent u a PM regarding my work.

p.s.

would i have to use mathematica or any other software for the conduct of research on population dynamics/dynamical models? i don't have one eh.
 
just PM me whenever you're online, ayt? thanks!

attached is a copy of my thesis proposal
 

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J77 said:
As it's an undergrad thesis, I'd advise you to take a well know model -- eg. http://en.wikipedia.org/wiki/Rössler_attractor -- and perform a bifurcation study; ie. with respect to showing you can do an analytical analysis, and write code to produce numerical bifurcation diagrams.

how do i do this?
 
butoyzki said:
how do i do this?
Well, the wiki link pretty much shows you how to linearize the equations and compute the eigenvalues which determine the stability of a steady state equilibrium.

For the numerics, look up some numerical integration schemes; such as, Euler or Runge-Kutta.

You could even do a survey of a number of nonlinear equations -- maps and flows -- and then use your code to compute numerical bifurcation diagrams.
 

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