Let's say I have a simple difference equation (the logistic equation from population dynamics);(adsbygoogle = window.adsbygoogle || []).push({});

[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.

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# A notation question

Can you offer guidance or do you also need help?

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