# A notation question

1. Sep 1, 2007

### PhDP

Let's say I have a simple difference equation (the logistic equation from population dynamics);

$$\frac{x_{t+1}}{x_t} = \alpha(t) - \beta x_t$$

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

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

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

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

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