@Preben Alsholm I apologize for being too vague and making you overworked yesterday. So basically

**a**= Is the growth rate of the prey (Elk)

**b= **rate at which the predator is successful to hunt the prey

**beta= **This is the death rate of the predator

**c=** Is the sussesfulness of the predator in terms of food consumption

**k= **Carrying capacity

Also I used data about the wolf project in yellowstone from 2010 given to to present day, in order to come up with an estimate of the parameters. **y **is 6000 because thats the number of Elk the Northern area of YNP started the year 2010. The same reason goes for **x **beign 40. Now I meant to say **t**= 0..40 (amount of time I want to predict the relationship). The first help you gave me actually gave me satisfactory results, since it was neat and resembled, for most part, the years from 2010 to 2014.

sys := (D(x))(t) = a*x(t)-a*x(t)^2/k-b*x(t)*y(t), (D(y))(t) = -beta*y(t)+c*x(t)*y(t);

res := dsolve({sys, x(0) = 6000, y(0) = 40}, numeric, parameters = [a, beta, k, b, c]);

res(parameters = [a = .71780, beta = .3067, b = 0.2072e-1, c = 0.9e-4, k = 20000]);

plots:-odeplot(res, [[t, x(t)], [t, y(t)]], 0 .. 40);

plots:-odeplot(res, [x(t), y(t)], 0 .. 30, view = [0 .. 7000, 0 .. 60])

#Thanks!!!!

However I still cannot make the dimensionless variables work. The lates help gives some errors. I even played around with it yesterday but I still got the same results. I will locate the errors where I highly believe they orginate.

restart;

sys := (D(x))(t) = a*x(t)-a*x(t)^2/k-b*x(t)*y(t), (D(y))(t) = -beta*y(t)+c*x(t)*y(t);

params := [a = .71780, beta = .3067, b = 0.2072e-1, c = 0.9e-4, k = 17000];

sol := dsolve({eval(sys, params), x(0) = 6000, y(0) = 40}, numeric);

plots:-odeplot(sol, [[t, x(t)], [t, 100*y(t)]], 0 .. 100, size = [1000, 300]);

# Error, (in plot/options2d) unexpected option: size = [1000, 300] (I know this one is not bad at all)

sol(100);

eqs := {T = 1/beta, X = k/(a*T), Y = beta/b, a = B*beta, k = a*A/c};

params := solve(eqs, {A, B, T, X, Y});

paramsConc := [a = .71780, beta = .3067, b = 0.2072e-1, c = 0.9e-4, k = 17000];

ABTXY := eval(params, paramsConc);

res := dsolve({SYS, u(0) = u0, v(0) = v0}, numeric, parameters = [u0, v0, A, B]);

# Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

L := subs(ABTXY, [6000/X, 40/Y, A, B]);

res(parameters = L);

input := subs(ABTXY, [[[tau, X*u(tau)], [tau, 100*Y*v(tau)]], tau = 0 .. 100/T]);

plots:-odeplot(res, op(input), size = [1000, 300]);

# Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

If you need more information that is needed to make this work I will tell you. I am grateful for the help man, thanks. I just want to see how dimensionless variable will work for this scenario.