>    #lab3

>    with(plots):#plotdisplay(inline);

>    alpha:=1:lambda:=0.03:beta:=0.4:mu:=0.01:
Eq:=[beta/mu,alpha/lambda]:Eqp:=pointplot(Eq,color=red):
ODE:=diff(C(t),t)=alpha*C(t)-lambda*C(t)*R(t),diff(R(t),t)=-beta*R(t)+mu*C(t)*R(t);
L:=15:c15:=dsolve([ODE,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2):

ODE := diff(C(t),t) = C(t)-.3e-1*C(t)*R(t), diff(R(t),t) = -.4*R(t)+.1e-1*C(t)*R(t)

>    A:=odeplot(c15,[t,C(t)],t=0..36,color=orange):
B:=odeplot(c15,[t,R(t)],t=0..36,color=blue):
display(A,B);

[Maple Plot]

>    C15:=odeplot(c15,[C(t),R(t)],t=0..12,color=red):
L:=20:c20:=dsolve([ODE,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2):
L:=25:c25:=dsolve([ODE,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2):
L:=30:c30:=dsolve([ODE,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2):
C20:=odeplot(c20,[C(t),R(t)],t=0..12,color=red):
C25:=odeplot(c25,[C(t),R(t)],t=0..12,color=red):
C30:=odeplot(c30,[C(t),R(t)],t=0..12,color=red):
display(C15,C20,C25,C30,Eqp);

[Maple Plot]

>    beta/mu;

40.00000000

>    for i from 0 to 36 by 0.2 do c15(i); od;

>    odeplot(c15,[C(t),R(t)],t=0..36,view=[35..45,10..13]);

>    alpha:=1.5:beta:=0.4:lambda:=0.03:mu:=0.01:L:=15:Eq2:=[beta/mu,alpha/lambda]:
Eq2p:=pointplot(Eq2,color=blue):
ODE2:=diff(C(t),t)=alpha*C(t)-lambda*C(t)*R(t),diff(R(t),t)=-beta*R(t)+mu*C(t)*R(t);alpha2:=dsolve([ODE2,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2);
display(C15,odeplot(alpha2,[C(t),R(t)],t=0..12,color=blue),title="alpha 1.5X carrots multiply faster",Eqp,Eq2p);

ODE2 := diff(C(t),t) = 1.5*C(t)-.3e-1*C(t)*R(t), diff(R(t),t) = -.4*R(t)+.1e-1*C(t)*R(t)

alpha2 := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; i...

[Maple Plot]

>    alpha:=1:beta:=0.8:lambda:=0.03:mu:=0.01:L:=15:Eq3:=[beta/mu,alpha/lambda]:
Eq3p:=pointplot(Eq3,color=blue):
ODE3:=diff(C(t),t)=alpha*C(t)-lambda*C(t)*R(t),diff(R(t),t)=-beta*R(t)+mu*C(t)*R(t);beta2:=dsolve([ODE3,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2);
display(C15,odeplot(beta2,[C(t),R(t)],t=0..12,color=blue),title="beta 2X rabbits leave faster",Eqp,Eq3p );

ODE3 := diff(C(t),t) = C(t)-.3e-1*C(t)*R(t), diff(R(t),t) = -.8*R(t)+.1e-1*C(t)*R(t)

beta2 := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if...

[Maple Plot]

>    alpha:=1:beta:=0.4:lambda:=0.06:mu:=0.01:L:=15:Eq4:=[beta/mu,alpha/lambda]:
Eq4p:=pointplot(Eq4,color=blue):
ODE4:=diff(C(t),t)=alpha*C(t)-lambda*C(t)*R(t),diff(R(t),t)=-beta*R(t)+mu*C(t)*R(t);lambda2:=dsolve([ODE4,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2);
display(C15,odeplot(lambda2,[C(t),R(t)],t=0..12,color=blue),title="lambda 2X rabbits eat carrots faster",Eqp,Eq4p);

ODE4 := diff(C(t),t) = C(t)-.6e-1*C(t)*R(t), diff(R(t),t) = -.4*R(t)+.1e-1*C(t)*R(t)

lambda2 := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; ...

[Maple Plot]

>    alpha:=1:beta:=0.4:lambda:=0.03:mu:=0.015:L:=15:Eq5:=[beta/mu,alpha/lambda]:
Eq5p:=pointplot(Eq5,color=blue):
ODE5:=diff(C(t),t)=alpha*C(t)-lambda*C(t)*R(t),diff(R(t),t)=-beta*R(t)+mu*C(t)*R(t);mu2:=dsolve([ODE5,C(0)=L,R(0)=L],numeric,range=0..36,initstep=0.2);
display(C15,odeplot(mu2,[C(t),R(t)],t=0..12,color=blue),title="mu 1.5X carrots have more value to rabbits",Eqp,Eq5p);

ODE5 := diff(C(t),t) = C(t)-.3e-1*C(t)*R(t), diff(R(t),t) = -.4*R(t)+.15e-1*C(t)*R(t)

mu2 := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _...

[Maple Plot]

>