具有扩散的3种竞争物种的图

Question

我想用扩散来制作一个竞争三种物种模型的代码来获得情节（2d绘制u，v，w对时间）我的模型是

u'=d1u_xx+(r1-a1u-b1v-c1w)u
v'=d2v_xx+(r2-a2u-b2v-c2w)v
w'=d3w_xx+(r3-a3u-b3v-c3w)w
where d1=d2=d3=1;
r1=1.5; r2=2.65; r3=3.45;
a1=0.1; b1=0.3; c1=0.01; b2=0.2;
a2=0.3; c2=0.2; c3=0.2; a3=0.01; b3=0.1.

我为此模型编写了代码而没有扩散，如下所示

% Define diff. equations, time span and initial conditions, e.g.
tspan = [0 20];
y0 = [0.2 0.2 0.2];

r1=1.5;     r2=2.65;    r3=3.45;
a1=0.1;     a2=0.3;     a3=0.01; 
b1=0.3;     b2=0.2;     b3=0.1;
c1=0.01;    c2=0.2;     c3=0.2; 

dy = @(t,y) [
(r1-a1*y(1)-b1*y(2)-c1*y(3))*y(1);
(r2-a2*y(1)-b2*y(2)-c2*y(3))*y(2);
(r3-a3*y(1)-b3*y(2)-c3*y(3))*y(3)];

% Solve differential equations
[t,y] = ode45(dy, tspan, y0);
 % Plot all species against time
figure(1)
plot(t,y)

结果如下图：

如何在this paper图10u，v，w

中进行扩散