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Math Help - {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations

  1. #1
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    {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations

    {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations-math2420_hw10_pr4.jpg

    I'm trying to evaluate this system, by finding and categorizing 4 equilibria points as stable, asymptotically stable, or unstable (nodes, saddles, foci, or centers). Then I have to determine if this describes a species coexistence or competitive exclusion scenario.

    I have found three of the 4 equil. points, and evaluated them in a Jacobi matrix. The fourth (positive equil. point) seems to not exist....as I solve the system to find that -0.5=0, which is obviously false.

    I'm afraid I may have made a mistake somewhere. Can I get a push in the right direction?
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  2. #2
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    Re: {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations

    I only get 3 roots for your system. What makes you think there is a fourth?
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  3. #3
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    Re: {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations

    Hi !
    The general solution of the EDOs system is shown in attachment.
    Attached Thumbnails Attached Thumbnails {x'=x(1-x-y), y'=y(1.5-x-y)} System of Differential equations-edossystem.jpg  
    Thanks from shane18
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