MATHEMATICAL BIOLOGY: I am trying to use MATLAB to code my predator-prey equations and plot them over time. (Lotka-Volterra model with extension of carrying capacity for prey) (you can use your own reasonable numbers for the variables/parameters in order to run the model). Please use MATLAB to code the following:

prey: dx/dt=rx(1-x/k)-axy

predator: dy/dt=caxy-qy

where x is the prey population, y is the predator population, t is time, r is the growth rate of prey,

a is the searching efficiency/attack rate of the predator, q is the predator mortality rate,

c is the predator efficiency at turning food into offspring (conversion efficiency),

and k is the carrying capacity of the prey.