Finding equilibrium points for an ODE system

8 views (last 30 days)
M
M on 20 Sep 2022
Commented: M on 21 Sep 2022
Hi, I have two functions named cdot and ctdot. I want to find the eqilibrium points which means cdot=ctdot=0. Could you please tell me how can I find points (c,ct) which satisfied in cdot=ctdot=0.
c and ct should be positive between [0,2].
Thanks in advance for any help.
vplc=0.16;
delta=0.1;
Ktau=0.045;
Kc=0.1;
K=0.0075;
Kp=0.15;
gamma=5.5;
kb=0.4;
vss=0.044;
alpha0=delta*6.81e-6/(0.002);
alpha1=delta*2.27e-5/(0.002);
Ke=7;
Vs=0.002;
ks=0.1;
Kf=0.18;
kplc=0.055;
ki=2;
A=(-(vss.*c.^2)./(ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));
h=(-(0.4.*A.*((Kc.^4).*(Kp.^2))./((p.^2.*c.^2.*gamma.*ct.*Kf))));
jin2=alpha1.*Kce.^4./((gamma.*ct).^4+Kce.^4);
p=(vplc.*c.^2/(c.^2+kplc.^2))./ki;
G1=alpha0+jin2;
G2=((1-h)./tau_max).*c.^4;
Fc=(4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);
Fct=((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Kce.^4)./(Kce.^4+(gamma.*ct).^4).^2);
Fh=(gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);
cdot=(Fct).*(G1)+(Fh).*(G2);
ctdot=-G1.*Fc;
  3 Comments
M
M on 21 Sep 2022
Yeah @Star Strider, it was posted before our discussion and because I wanted to see the figures I preferred to post the question separately.

Sign in to comment.

Answers (1)

KSSV
KSSV on 20 Sep 2022
Edited: KSSV on 20 Sep 2022
tol = 10^-5 ; % change the tolerance
idx = abs(cdot)<tol & abs(cddot)<tol ;
[cdot(idx) cddot(idx)]
  2 Comments
KSSV
KSSV on 21 Sep 2022
Edited: KSSV on 21 Sep 2022
Try changing the tolerance value.

Sign in to comment.

Categories

Find more on Creating and Concatenating Matrices in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!