I have adajacency matrix B. Now ,I want to write a matlab code for time series .I have written some part of the code

clc;

clear all;

n = 10;

C= zeros(n, n);

C(1,n)=1;

C(1,n-1)=1;

C(2,n)=1;

A = zeros(n, n);

for i = 1:n

for j = 1:n

if j==i+1 || j == i + 2

A(i,j) = 1;

else

A(i, j) = 0;

end

end

end

B1=A+C;

B=B1+B1';

% Parameters

% matrixSize = 10; % Size of the matrix

numEdgesToRewire = 3; % Number of edges to rewire

% Create an initial matrix

% Y = B;

matrixSize=10;

% Randomly select two edges to rewire

edgesToRewire = randperm(matrixSize, numEdgesToRewire);

% Iterate through the edges to rewire

for i = 1:numEdgesToRewire

node1 = edgesToRewire(i);

node2 = randi([1, matrixSize]);

% Avoid rewiring to the same node or existing edges

while node2 == node1 || B(node1, node2) == 1

node2 = randi([1, matrixSize]);

end

% Rewire the edge

B(node1, node2) = 1;

B(node2, node1) = 1;

end

% Display the rewired matrix

disp(B);

%%

function xprime = kau(t,x,B)

theta=0.3;dh=2^-9;dp=2^-7;phi=3;ita=1;

n=10;

% nn=n*d;

f=[];

for i=1:n;

y1=[x(1);x(3);x(5);x(7);x(9);x(11);x(13);x(15);x(17);x(19)];

y2=[x(2);x(4);x(6);x(8);x(10);x(12);x(14);x(16);x(18);x(20)];

f= [f; x(2i-1)*(1-theta*x(2i-1))-(x(2i))-(x(2i-1)*x(2i))/(1+x(2i))+dh*B*y1;...,

(phi*x(2i-1)*x(2i))/(1+x(2i))-ita*x(2i)+dp*B*y2];

end

end

xprime=f-B*y

x0=[h0,p0];

h0=rand(10,1);

p0=rand(10,1);

[t,xsol]=ode45(kau,[0 100],x0);

solutions=[];

% h=rand(10,1);

% p=rand(10,1);

H=sum(y1);

P=sum(y2);

plot(t,H,'b');

plot(t,P,'r');

Answer 1

[Divyam]

Hi @mks,

The code uses a deterministic method for rewiring the adjacency matrix and can cause issues such as self looping and duplication of edges. Rewiring the edges randomly will fix this issue. Here is a sample code that can be modified as per your specific requirements:

clc;
clear all;

% Parameters
n = 10; 
numEdgesToRewire = 3; % Number of edges to rewire

% Create adjacency matrix B
C = zeros(n, n);
C(1, n) = 1;
C(1, n-1) = 1;
C(2, n) = 1;
A = zeros(n, n);
for i = 1:n
    for j = 1:n
        if j == i + 1 || j == i + 2
            A(i, j) = 1;
        end
    end
end
B1 = A + C;
B = B1 + B1';

% Rewire edges
edgesToRewire = randperm(n, numEdgesToRewire);
for i = 1:numEdgesToRewire
    node1 = edgesToRewire(i);
    node2 = randi([1, n]);
    
    % Avoid rewiring to the same node or existing edges
    while node2 == node1 || B(node1, node2) == 1
        node2 = randi([1, n]);
    end
    
    % Rewire the edge
    B(node1, node2) = 1;
    B(node2, node1) = 1;
end

% Display the rewired matrix
disp('Rewired adjacency matrix B:');
disp(B);

% Initial conditions
h0 = rand(n, 1);
p0 = rand(n, 1);
x0 = [h0; p0];

% Solve the differential equations
[t, xsol] = ode45(@(t, x) kau(t, x, B), [0 100], x0);

% Extract solutions
H = sum(xsol(:, 1:n), 2);
P = sum(xsol(:, n+1:end), 2);

% Plot the results
figure;
plot(t, H, 'b', 'DisplayName', 'H(t)');
hold on;
plot(t, P, 'r', 'DisplayName', 'P(t)');
xlabel('Time');
ylabel('Population');
legend;
title('Time Series of H and P');
hold off;

% Function defining the differential equations
function xprime = kau(t, x, B)
    theta = 0.3;
    dh = 2^-9;
    dp = 2^-7;
    phi = 3;
    ita = 1;
    n = 10;
    
    y1 = x(1:n);
    y2 = x(n+1:end);
    
    f = zeros(2*n, 1);
    for i = 1:n
        f(i) = y1(i) * (1 - theta * y1(i)) - y2(i) - (y1(i) * y2(i)) / (1 + y2(i)) + dh * (B(i, :) * y1);
        f(n+i) = (phi * y1(i) * y2(i)) / (1 + y2(i)) - ita * y2(i) + dp * (B(i, :) * y2);
    end
    
    xprime = f;
end

Here, using the "randperm" method, you can randomly select the number of edges to rewire and remove the possibility of self looping, for more information about the "randperm" function refer to this documentation: https://www.mathworks.com/help/matlab/ref/randperm.html