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Math Help - Dynamical system

  1. #1
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    Dynamical system

    I'm given

    F' = 0.01F(10-F-3R)
    R' = 0.0125R(8-R-2F)
    F' = 0.1F(1 - F/10) - 0.03FR
    R' = .1R (1 - R/8) - 0.025FR


    I have to find the four equilibrium points for the system. I'm a little confused about how to do this so if anyone could be of assistance, I would REALLY appreciate it!
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  2. #2
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    can u solve this answer by any means? or do u want a nice analytical solution?
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  3. #3
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    I got a question.
    What does that Dynamical System represent?

    Is it a differencial equation system (not a linear system, I can see that)?

    I am asking this because I want to know what a dynamical system is.
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  4. #4
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    Well, that particular dynamical system represents a mathematical model of competition, in which two species, wolves and tigers, compete for the same resources. F represents the wolf population, in hundreds of wolves, and R represents the tiger population in hundreds of tigers.

    I should have mentioned that before - sorry.
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  5. #5
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    rite ill try and solve it
    Last edited by chogo; March 29th 2007 at 02:58 PM.
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  6. #6
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    ok, thanks!
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  7. #7
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    Actually, don't worry about it. I just figured out how to find the points.

    I do have a question, though. What is the significance of the term - 0.03FR in the F' equation and of the term -0.025FR in the R' equation?
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  8. #8
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    This question ur asking is called the Lotka-volterra model of competition. Its a famous example in ecology of two competing species. Both wolves and tigers are both competing for the same resources.

    The FR terms represent when wolves and tigers encounter each other. Trouble starts. Sometimes the tigers get to eat, but more usually the wolves get preference over food. The reason the wolves get preference usually is that it is assumed that these conflicts occur at a rate proportional to the size of each population. As u can see the coefficient for wolves(0.03) is more than that for tigers(0.025).

    Hope that answers ur question.

    Do u still want me to solve the equation to check ur answers

    also you said this was a dynamical system problem, do you need to do stability analysis involving jacobians and finding types of stability using eigen values etc?
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