As you already know, lynx are predators of hares and a balance between the populations of these two animals is necessary, so that the populations have a stable growth.
As you can see in the chart above, when the lynx population is very low, the hare population is high. This is because, as there are few lynxes, predation is low and hares are able to maintain their birth rate higher than the mortality rate. However, there are many hares available for lynx to feed on, which allows the lynx's birth rate to also be higher than the mortality rate, which causes the lynx population to grow.
Also according to the graph, you can see that as the lynx population grows, the hare population decreases. This is because the greater number of lynx causes predatorism to increase and hares are hunted by lynx in greater quantities. This causes the mortality rate of hares to be higher than the birth rate, which decreases its population. On the other hand, the abundance of food allows the lynx population to grow to some extent. This is because, as you can see in the graph, when the hares population is very small, the lynx does not have enough food, which causes an increase in the mortality rate, also decreasing the lynx population.
When the lynx population is low, predatorism is lower, which allows hares to reproduce by increasing their population, which will result in an increase in the lynx population.
