The logistic population growth is expressed by the equation:

1. $\frac{dN}{dt}=rN\left(\frac{N-K}{N}\right)$

2. $\frac{dt}{dN}=Nr\left(\frac{K-N}{K}\right)$

3. $\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$

4. $\frac{dN}{dt}=rN$

The population of an insect species shows an explosive increase in numbers during the rainy season followed by its disappearance at the end of the season. What does this show?