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Math Help - Brusselator equation

  1. #1
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    Brusselator equation

    The Brusselator equation is

    \frac{d[X]}{dt} = k_1[A] - k_2[b][X] - k_4[X] + k_3[X]^2[Y]

    \frac{d[Y]}{dt} = k_2[b][X] - k_3[x]^2[Y]

    by linear scaling the variables and time, we have

    \frac{dx}{dt} = a - (b + 1)x + x^2y

    \frac{dy}{dt} = bx - x^2y

    but how do we do it? what substitusion should I use?

    thx for any help
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  2. #2
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    Quote Originally Posted by dedust View Post
    The Brusselator equation is

    \frac{d[X]}{dt} = k_1[A] - k_2[b][X] - k_4[X] + k_3[X]^2[Y]

    \frac{d[Y]}{dt} = k_2[b][X] - k_3[x]^2[Y]

    by linear scaling the variables and time, we have

    \frac{dx}{dt} = a - (b + 1)x + x^2y

    \frac{dy}{dt} = bx - x^2y

    but how do we do it? what substitusion should I use?

    thx for any help
    Let [X] = \alpha x,\;\; [Y] = \beta y,\;\; t = \gamma \tau substitute and isolate

    \frac{d x}{d \tau} and  <br />
\frac{d y}{d \tau}<br />

    Then compare with

    \frac{dx}{dt} = a - (b + 1)x + x^2y

    \frac{dy}{dt} = bx - x^2y

    literally term by term. This will give you three equations for your unknowns \alpha, \beta \; \text{and}\; \gamma.
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