How to plot nullclines with differential equations

2021 10 4
1 个回答
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更新时间：2021 10 4
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1 个投票

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!

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 采纳的回答

Star Strider
Star Strider 2021-10-4
Ran in:

0 个投票

Ran in:
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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