In the predator-prey relationship given, the populations would be modeled by two differential
equations. The Matlab command ode45 will then be used to solve the system of differential
equations. We will consider the predators and the prey as having constant birth and death rates. If
the fox population only feeds on rabbits and has a population of x(t) at time t, when there are no
rabbits at all, the fox population will die out as per the differential x’= -dx where d is the birth
rate less the death rate. The rabbit population y(t) will, with no foxes, continue to increase for
some time as per the differential equation y’=by where b is the birth rate less the death rate. We
would like to model a case where both the populations are positive as per the Lotka-Volterra
system of differential equations, i.e.
x' = (-d + ey)x and x(0) = x0……………….Fox equation
y' = (b - cx)y and y(0) = y0…………………Rabbit equation
we can substitute the above equations in the below Lotka-Volterra system of differential
x’=0.06x – 0.0004yx
y'= -0.08y + 0.0002xy such that;
x’= (-d+ey)x=0.06x – 0.0004yx. We get d=-0.06 and e =-0.0004
y’=(b-cx)y =(-0.08+0.0002yx). Simplifying we get ...