Question

The Mongolian reef is divided into 7 different sectors, which are populated by Kernighans and Ritchies.
Ritchies are the only food for Kernighans, and Kernighans the only predators of Ritchies. This predator-prey
relationship determines largely the population size. However, the population is also influenced by migration of
fish. Measurements show that every month a certain fraction in a sector will migrate to a neighbouring sector.

Population Model
Suppose that in a given month the number of Kernighan in sector i is pop_k[i], and the population of Ritchies is pop_r[i]. The number of Kernighans in sector i changes as follows:
• The population pop_k[i] decreases by alpha_k · pop_k[i]. This is the number of Kernighans that
would starve if there were no Ritchies to eat.
• The population pop_k[i] increases by beta_k · pop_k[i] · pop_r[i]. This is the number of new
Kernighans because they can feed on Ritchies.
• The population pop_k[i] decreases by gamma_k · pop_k[i]2. This decrease in the number of
Kernighans is