In: Advanced Math
Consider an ecological niche with three species A, B and C. Their dynamics are given by their population rates shown below
dA/dt=A+B-C … (2a)
dB/dt=-A+2B … (2b)
dC/dt=C-A-B … (2c)
Initially, the niche is in equilibrium with the population of C=30. Obtain the population densities of the rest of participants in the niche at its equilibrium. Starting from the point (A=8,B=4,C=10), obtain their individual populations over time t. What if the initial starting point is perturbed to (A=7,B=4,C=10)? Would the system emerge in the same way?