I want to plot phase diagram .But I reach here maintion the code below please help ,me the remaining part

clc;clear;close all;
r=0.1;
k=50;
a=0.01;
e=0.5;
m=0.05;
s=0.1;
w=0.1;
b=0.001;
q=0.03;
F=1.;
M=50;
X=0:1:50;J=[0 50 0 20];

Pi_0=(w/(w+b*M))*(F/s);Pi_1=((w+b*M)/w)*(F/s);
D1=Pi_0+0*X;D2=Pi_1+0*X;
plot(D1,X,'k--')
axis(J)
hold on
plot(D2,X,'k--')
X1=(Pi_0/99);X2=(Pi_1-Pi_0)/99;X3=(50-Pi_1)/99;Y2=20/99;

P1=0:X1:Pi_0;H1=0:Y2:20;P2=Pi_0:X2:Pi_1;H2=0:Y2:20;P3=Pi_1:X3:50;H3=0:Y2:20;

u_1=0;u_2=((s.*P2)/(s.*P2+F)+(w*(s.*P2-F))/(b*M*(s.*P2+F)));u_3=1;

f = @(P1,H1) (r.*P1).*(1-P1/k)-(a.*P1.*H1)./(1+q*u_1*M);
fimplicit(f,[0 Pi_0 0 20],'g')
hold on
f1 = @(P1,H1) (e*a.*P1.*H1)./(1+q*u_1*M)- m.*H1;
fimplicit(f1,[0 Pi_0 0 20],'g')
hold on

%%
[P1, H1] = meshgrid(0, 0:0.01:Pi_0);

dP1dt = dP1(P1, H1);

Unrecognized function or variable 'dP1'.

dH1dt = dH1(P1, H1);

quiver(P1, H1, dP1dt, dH1dt, 'color', 'b');

f = @(P2,H2) (r.*P2).*(1-P2/k)-(a.*P2.*H2)./(1+q*((s.*P2)/(s.*P2+F)+(w*(s.*P2-F))/(b*M*(s.*P2+F)))*M);
fimplicit(f,[Pi_0 Pi_1 0 20],'r')
hold on
f1 = @(P2,H2) (e*a.*P2.*H2)./(1+q*((s.*P2)/(s.*P2+F)+(w*(s.*P2-F))/(b*M*(s.*P2+F)))*M)- m.*H2;
fimplicit(f1,[Pi_0 Pi_1 0 20],'r')
hold on

%%
[P2, H2] = meshgrid(0:0.01:Pi_0, 0:0.01:Pi_1);

dP2dt = dP2(P2, H2);
dH2dt = dH2(P2, H2);

quiver(P2, H2, dP2dt, dH2dt, 'color', 'b');

Answer 1

[Shlok]

As per my understanding, you want to plot the full phase diagram for your system by showing how the system evolves over time. I suggest following approach to complete the above code:

• Define the system’s differential equations ("dP/dt" and "dH/dt").
• Create a grid over the phase space using "meshgrid".
• Evaluate the derivatives at each grid point.
• Use "quiver" to plot the direction field that shows the flow of the system.

Hence, the code can be completed by following the above steps. This gives a complete visual representation of both the equilibrium lines and the system’s behavior in each region.

Refer to the following MathWorks documentation links to know more about "meshgrid" and "quiver" functions:

• https://www.mathworks.com/help/matlab/ref/meshgrid.html
• https://www.mathworks.com/help/matlab/ref/quiver.html