# Question:how to fix this error in Equilibrium point for nonlinear ode

## Question:how to fix this error in Equilibrium point for nonlinear ode

Maple

sigma1:=10^(-5):sigma2:=10^(5):sigma3:=3.7*10^(6):alpha:=5*10^(-7):beta1:=0.5*10^(-4):beta2:=0.5*10^(-4):beta3:=0.5*10^(-4):ky:=1:kz:=10^4:mu1:=10:mu2:=11:mu3:=0.86:mu4:=0.2:mu5:=1:v1:=0.5:v2:=1:alphaa:=0.6:alphas:=0.24:alphad:=0.16:A:=0.5:mus:=0.17:k:=0.2:#parameters
dsys:={diff(x1(t),t)=sigma1*y(t)-beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))-v1*x1(t)-mu1*x1(t)+(2*alphad+alphaa)*k*A*S(t),diff(x2(t),t)=v1*x1(t)-beta2*x2(t)*y(t)/(ky+x1(t)+x2(t))+alpha*v2*x1(t)*z(t)-mu2*x2(t),diff(y(t),t)=sigma2*(beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))+beta2*x2(t)*y(t)/(ky+x1(t)+x2(t)))-mu4*y(t)-mu5*y(t)^2,diff(z(t),t)=sigma3+y(t)*beta3/(kz+y(t))-mu3*z(t)-v2*z(t)*x2(t),diff(S(t),t)=(k*(alphas-alphad)-mus)*S(t) }; #SYS ODE

rhs; with(DEtools);# to find the equilibrium points
fx1 = sigma1*y-beta1*x1*y-v1*x1-mu1*x1+(2*alphad+alphaa)*k*A*s; fx2 = alpha*v2*x1*z-beta2*x2*y-mu2*x2+v1*x1; fy = sigma2*(beta1*x1*y+beta2*x2*y)-mu4*y-mu5*y^2; fz = sigma3+y*(kz+y)-mu3*z-v2*z*x2; fs = (k*(alphas-alphad)-mus)*s;

eqs := solve({fs, fx1, fx2, fy, fz}, {s, x1, x2, y, z})

L := map(subs, [eqs], [x1, x2, y, z, s])

J := unapply(VectorCalculus:-Jacobian([fx1, fx2, fy, fz, fs], [x1, x2, y, z, s]), x1, x2, y, z, s); J(x1, x2, y, z, s)

﻿