# Question:CharacteristicPolynimial

## Question:CharacteristicPolynimial

Maple

I could not figure how to fix my code. Could you help me?

LinearAnalysis.mw

 > restart;
 > :with(DynamicSystems):with(DEtools):with(plots):with(plottools):with(DETools):
 > wiht(LinearAlgebra): with(VectorCalculus):
 >
 >
 > e1:=0.5: e2:=0.2:
 > sigma1:=e1*alpha: sigma2:=e2*delta:
 > g:=x/(1+beta*x^2); f:=(theta*x-1)*(1-x)*(1+beta*x^2)-y; h:=alpha*g-z-sigma1; j:=delta*y-sigma2; F:=g*f; H:=y*h; G:=z*j;
 (1)
 >
 > theta:=5;alpha:=1;delta:=1;beta:=0.4; Ffunc:=unapply(F,x,y); Hfunc:=unapply(H,x,y,z);Gfunc:=unapply(G,y,z); J1:=Jacobian([Ffunc(x,y),Hfunc(x,y,z),Gfunc(y,z)],[x,y,z]); C:= CharacteristicPolynomial(J1,lambda); R:= RouthTable(C,lambda);
 (2)
 > E0:= [0,0,0]; JE0:=subs(x=E0[1],y=E0[2],z=E0[3],J1); CE0:=CharacteristicPolynomial(JE0,lambda); RE0:= RouthTable(CE0,lambda); RouthTable(CE0,lambda,'stablecondition'=true);
 (3)
 > E1:= [1,0,0]; JE1:=subs(x=E1[1],y=E1[2],z=E1[3],J1); CE1:=CharacteristicPolynomial(JE1,lambda); RE1:= RouthTable(CE1,lambda); RouthTable(CE1,lambda,'stablecondition'=true);
 (4)
 > E2:= [1/theta,0,0]; JE2:=subs(x=E2[1],y=E2[2],z=E2[3],J1); CE2:=CharacteristicPolynomial(JE2,lambda); RE2:= RouthTable(CE2,lambda); RouthTable(CE2,lambda,'stablecondition'=true);
 (5)
 >