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Im trying to plot stable and unstable equilibrium solutions for my graph but Im not sure where or how to use the fzero function to do so for dx1 and dx2

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Zachary David
Zachary David 2021-10-6
close all; clear all;
% This Matlab code generates a vector field for the system of ODEs
% dx1/dt = f(x1,x2), dx2/dt = g(x1,x2)
x1min = -1; x1max = 6; x2min = -1; x2max = 6;
x1step = 0.5; x2step = 0.5;
[x1, x2] = meshgrid(x1min:x1step:x1max, x2min:x2step:x2max);
a = 1.5;
b = 1.1;
g =2.5;
d =1.4;
dx1 = -a.*x1+b.*x1.*x2;
dx2 = g.*x2-d.*x1.*x2;
dx1 = dx1./sqrt(dx1.^2 + dx2.^2);
dx2 = dx2./sqrt(dx1.^2 + dx2.^2);
axis([x1min x1max x2min x2max]);
xlabel('$x1$','Interpreter','latex')
ylabel('$x2$','Interpreter','latex')
title('Vector field example','Interpreter','latex')
nullX1= -a + b.*x2;
nullX2= g - d.*x1;
x=linspace(-1,6,size(nullX1,1));
quiver(x1, x2, dx1,dx2,'AutoScaleFactor',0.5)
hold on
plot(x,nullX1,'r-')
hold on
plot(x,nullX2,'k-')
hold on
legend('flow','nullX1','nullX2')
[t,x] = ode45(@ODE45Fun,[0,30],[0.5,1]);
plot(t,x(:,1),'g-',t,x(:,2),'b-')
hold on
fzero(dx1,0)
grid
xlabel('Number of Years')
ylabel('Predator-Prey Pop.')
title('Lotka Voltera Pred-Prey Pop.Figure1')

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