How to plot nullclines with differential equations

Im trying to plot nullclines on top of a mesh grid then use ode 45

i cant seem to get the nullclines on their though after googling for hours. This is my code:

x1min = -1; x1max = 6; x2min = -1; x2max = 6;

x1step = 0.3; x2step = 0.3;

[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;

nullX1= -a + b.*x2;

nullX2= g - d.*x1;

quiver(x1, x2, dx1,dx2,'AutoScaleFactor',0.5)

axis([x1min x1max x2min x2max])

xlabel('$x1$','Interpreter','latex')

ylabel('$x2$','Interpreter','latex')

title('Vector field example','Interpreter','latex')

x=0:0.5:30;

plot(x,nullX1,'r-')

hold on

plot(x,nullX2,'k-')

hold on

*****It keeps telling my my vectors must be the same length, so not sure if im using the wrong parameters.

Thanks!

Answer 1

[Star Strider]

Work-around —

x = linspace(0, 30, size(nullX1,1)); % Use 'linspace' To Create Correct Length 'x'

x1min = -1; x1max = 6; x2min = -1; x2max = 6;
x1step = 0.3; x2step = 0.3; 
[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; 
nullX1= -a + b.*x2

nullX1 = 24×24

-2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.6000 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -2.2700 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.9400 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.6100 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -1.2800 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.9500 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.6200 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 -0.2900 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700 0.3700

nullX2= g - d.*x1

nullX2 = 24×24

3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600 3.9000 3.4800 3.0600 2.6400 2.2200 1.8000 1.3800 0.9600 0.5400 0.1200 -0.3000 -0.7200 -1.1400 -1.5600 -1.9800 -2.4000 -2.8200 -3.2400 -3.6600 -4.0800 -4.5000 -4.9200 -5.3400 -5.7600

quiver(x1, x2, dx1,dx2,'AutoScaleFactor',0.5)
axis([x1min x1max x2min x2max])

xlabel('$x1$','Interpreter','latex')
ylabel('$x2$','Interpreter','latex')
title('Vector field example','Interpreter','latex')

% x=0:0.5:30;
x = linspace(0, 30, size(nullX1,1));                    % Use 'linspace' To Create Correct Length 'x' 
plot(x,nullX1,'r-')
hold on
plot(x,nullX2,'k-')
hold on

Experiment to get different results.

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