System dravec-korist (Lotka-Volterra) 

>	with(plots);

 

>	unprotect(gamma);

 

Parametry: 

>	alpha := 1; beta  := 0.1; gamma := 1; delta := 0.1;

 

System rovnic: 

>	sys := {diff(x(t),t)= x(t)*(alpha - beta*y(t)), diff(y(t),t)= -y(t)*(gamma - delta*x(t))};

 

Pocatecny podminky: 

>	pocatecni := {x(0)=10, y(0)=4};

 

Numericke reseni: 

>	q:= combine(dsolve(sys union pocatecni,{x(t), y(t)}, type=numeric, range=0..10)):

 

Vykresleni reseni: 

>	odeplot(q, [[t,x(t),color=green, thickness=3], [t,y(t),color=red, thickness=3]]);

 

>	odeplot(q, [x(t),y(t)],color=blue, thickness=3, numpoints=100);

 

Charakteristicke vektorove pole (integralni krivky jsou charakteristiky): 

>	fieldplot([x*(alpha - beta*y),-y*(gamma - delta*x)],x=0..22,y=0..22,arrows=SLIM, color=orange);

 

>	display(%,%%);

 

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