Find the turing pattern for following equation

the equation is

dx/dt={r/(1-ky) - r0-r1x-[alpha*(1-beta*y)*x]/[a+(1-beta*y)*x]}x

dy/dt={[new-cy/[a+(1-beta*y)*x]}*y

[John D'Errico]

Since this is highly likely to be a homework asignment, what have you done? What effort have you made? If none, then we cannot help you. And we cannot do your homework anyway. Aanyway, your question is not a question about MATLAB, beyond asking us to write the code to solve your problem.

https://en.wikipedia.org/wiki/Turing_pattern

[Abhay]

i just wanted a turing code to solve a question so i asked a simple version to get an idea

If you know any other equation turing code please share it

Answer 1

[John D'Errico]

I won't do your homework, since this is highly likely to be homework with no effort made on your part, just from the way you asked the question. However, since you ask for a example code, all you had to do was a direct search for "turing pattern MATLAB", and you would find this:

https://blogs.mathworks.com/graphics/2015/03/16/how-the-tiger-got-its-stripes/

And there you will find a complete example of how to generate a Turing pattern, fully done in MATLAB.

[Abhay]

thank you

[Abhay]

i have tried something but i am unable to get the graph plotting can you help me with this

i will be attaching my code here

function hyhy(n)

n=100;

time=10000; d1=0.1; d2=4; tau=1; h=1/3;

r=3.5; r2=1; r1=0.5; alpha=2; a=0.3; mew=1; c=0.9;

beta=0.7; k=0.8; y=9.22;

a1=alpha*k*mew^2*beta^2;

a2=r1*k*c^2+alpha*mew^2*beta*(beta-2*k)-c*r2*mew*k*beta;

a3=c*r*mew*beta+c*r2*mew*(k-beta)+r1*c*(c-a*mew*k)-alpha*mew^2*(2*beta-k);

a4=mew*(c*r2+alpha*mew-c*r-c*r1*a);

R=roots([a1 a2 a3 a4]);

ii = 0;

for i=1:length(R)

if real(R(i))>0 && imag(R(i))<0.00001

ii = ii+1;

RR(ii) = R(i);

end

end

number_of_positive_equilibrium=length(RR);

p1=RR(2);

n1=(c*p1-mew*a)/(mew*(1-beta*p1));

u=n1+5*0.0001*rand(n,n); grad1=u*0;

v=p1+5*0.0001*rand(n,n); grad2=v*0;

for step=1:time

I = 2:n-1; J = 2:n-1;

grad1(I,J)= (u(I,J-1)+u(I,J+1)+u(I-1,J)+u(I+1,J)-4*u(I,J))/h^2;

grad2(I,J)= (v(I,J-1)+v(I,J+1)+v(I-1,J)+v(I+1,J)-4*v(I,J))/h^2;

u = u + tau * (d1 * grad1 + (r ./ (1 + k * v) - r2 - r1 * u - (alpha * (1 - beta * v) .* v) ./ (a + (1 - beta * v) .* u)) .* u);

v = v + tau * (d2 * grad2 + (mew - (c * v) ./ (a + (1 - beta * v) .* u) .* v) );

step;

end

pcolor(u);

shading interp;

colorbar;

colormap jet;

drawnow;

zoom(2);

axis off;

set(gcf, 'renderer', 'zbuffer');