Устойчивость

> if steady(0,0,2,6,4,1,4,.1)=1 then print(`(0,0)-Steady`):else print(`(0,0)-UnSteady`):fi;

> if steady(0,4,2,6,4,1,4,.1)=1 then print(`(0,4)-Steady`):else print(`(0,4)-UnSteady`):fi;

> if steady(6,0,2,6,4,1,4,.1)=1 then print(`(6,0)-Steady`):else print(`(6,0)-UnSteady`):fi;

> dfieldplot([D(x)(t)=f_11(x,y,t),D(y)(t)=f_22(x,y,t)],[x(t),y(t)],t=-10..10,x=0..5,y=0..5,title=`{dx/dt=f_11(x,y),dy/dt=f_22(x,y)}`);

> phaseportrait([D(x)(t)=f_11(x,y,t),D(y)(t)=f_22(x,y,t)],[x(t),y(t)],0..10,[[x(0)=.2,y(0)=.2]],stepsize=.05,scene=[x(t),y(t)],linecolour=sin(t*Pi/2),method=classical[foreuler],title=`{dx/dt=f_11(x,y),dy/dt=f_22(x,y)} {x(0)=0.2,y(0)=0.2}`);

> F:=dsolve({D(x)(t)=f_11(x,y,t),D(y)(t)=f_22(x,y,t),x(0)=4.5,y(0)=4.5},{x(t),y(t)},type=numeric);

> g_1:=plots[odeplot](F,[t,x(t)],0..6,labels=[t,x],color=red):

> g_2:=plots[odeplot](F,[t,y(t)],0..6,labels=[t,y],color=blue):

> g_3:=plot(4,0..5,color=green):

> display({g_1,g_2,g_3},title=`First kind-red, second kind-blue`);

(Ненулевое равновесное состояние)

L_1 и L_2 пересекаются в положительном квадранте и L_1 круче падает чем L_2.

> L_11:=plot(subs({K_1=4.5,a_12=.1},L_1),x=0..10,y=0..30):

> L_22:=plot(subs({K_2=5,a_21=.1},L_2),x=0..50,y=0..10,color=blue):

> display({L_11,L_22},title=`Red-L_1, blue-L_2`);

> f_11:=unapply(subs({r_1=2,K_1=4.5,a_12=.1},f_1),x,y);

> f_22:=unapply(subs({r_2=1,K_2=3,a_21=.1},f_2),x,y);

> fixed:=solve({f_11(x,y)=0,f_22(x,y)=0},{x,y});