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A notation question

  1. Sep 1, 2007 #1
    Let's say I have a simple difference equation (the logistic equation from population dynamics);

    [tex]
    \frac{x_{t+1}}{x_t} = \alpha(t) - \beta x_t
    [/tex]

    Now, let's say [tex]\alpha(t)[/tex] depends on the time of the year, and t = 3 months, I could built a vector for the value of [tex]\alpha(t)[/tex] for the year;

    [tex]
    \alpha =
    \left[\begin{array}{c}
    1.0\\1.2\\1.5\\1.1
    \end{array}\right]
    [/tex]

    Now, obviously, at time t=5, it would have to get back to [tex]\alpha(1)[/tex]. I was thinking about using something like;

    [tex]
    \frac{x_{t+1}}{x_t} = \alpha([(t-1) \mbox{ mod}(4)]+1) - \beta x_t
    [/tex]

    But I wondered if there was a better notation for this.
     
  2. jcsd
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