Matlab coding ordinary differential equation initial condition graph not running in the initial condition
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Matlab coding ordinary differential equation initial condition graph not running in the initial condition. For x(2), x(6) and x(7) only getting properly graph is coming with the initial condition starting but for x(1), x(3), x(4), x(5) graph is not coming as the initial condition starting
Tr()
function Tr
options = odeset('RelTol',1e-6,'Stats','on');
%initial conditions
Xo = [0.005; 0.0007; 0.001; 0.0001; 0.0001; 0; 0];
tspan = [0,120];
tic
[t,X] = ode45(@TestFunction,tspan,Xo,options);
toc
%figure
hold on
plot(t, X(:,1), 'green')
plot(t, X(:,2), 'blue')
plot(t, X(:,3), 'red')
plot(t, X(:,4), 'yellow')
plot(t, X(:,5), 'green')
plot(t, X(:,6), 'cyan')
plot(t, X(:,7), 'y')
%hold on
% legend('x1','x2')
% ylabel('x - Population')
% xlabel('t - Time')
%hold on
end
function [dx_dt]= TestFunction(~,x)
% Parameters
s = 0.038;
alpha = 0.02;
gamma = 0.10;
r = 0.03;
dH = 0.0083;
dX = 0.0125;
rho = 0.07;
K = 500;
beta = 0.0005;
theta = 0.03;
eta = 0.015;
muH = 0.015;
muI = 0.08;
lambdaP = 0.05;
lambdaL = 0.043;
UP = 0.20;
deltaP = 0.033;
UL = 0.50;
deltaL = 0.05;
kappa = 0.005;
dx_dt(1) = (s) - ((alpha * x(3) * x(1)) / (1 + gamma * x(1))) - (dH * x(1)) + (r * x(2));
dx_dt(2) = ((alpha * x(3) * x(1)) / (1 + gamma * x(1))) - ((r+dX) * x(2));
dx_dt(3) = ((rho * x(3)) * (1 - (x(3) + x(4)) / K)) - (beta * x(3) * x(5)) - (lambdaP * x(6) * x(3)) - (lambdaL * x(7) * x(3)) - (muH * x(3));
dx_dt(4) = (beta * x(3) * x(5)) - (lambdaP * x(6) * x(4)) - (lambdaL * x(7) * x(4)) - (muI * x(4)) - (kappa * x(5) * x(4));
dx_dt(5) = (theta * x(4)) - (eta * x(5));
dx_dt(6) = (UP) - (deltaP * x(6));
dx_dt(7) = (UL) - (deltaL * x(7));
dx_dt = dx_dt';
end
%hold on
4 个评论
The responses for x1, x3, x4, and x5 begin from the specified initial values: {0.005, 0.001, 0.0001, 0.0001}.
options = odeset('RelTol', 1e-6);
X0 = [0.005; 0.0007; 0.001; 0.0001; 0.0001; 0; 0];
% x1 x2 x3 x4 x5 x6 x7
tspan = [0, 120];
[t, X] = ode45(@TestFunction, tspan, X0, options);
% figure(1)
% tL = tiledlayout(2, 2, 'TileSpacing', 'Compact');
%
% nexttile
% plot(t, X(:,1), 'color', '#AA0815'), grid on
% title('x1')
%
% nexttile
% plot(t, X(:,3), 'color', '#F0B41C'), grid on
% title('x3')
%
% nexttile
% plot(t, X(:,4), 'color', '#49B6A9'), grid on
% title('x4')
%
% nexttile
% plot(t, X(:,5), 'color', '#3D9BE1'), grid on
% title('x5')
%
% xlabel(tL, 'Time')
% ylabel(tL, 'Population')
figure(2)
tL2 = tiledlayout(2, 2, 'TileSpacing', 'Compact');
nexttile
plot(t, X(:,1), 'color', '#AA0815'), grid on
xlim([0, 120])
title('x1')
nexttile
plot(t, X(:,3), 'color', '#F0B41C'), grid on
xlim([0, 120])
title('x3')
nexttile
plot(t, X(:,4), 'color', '#49B6A9'), grid on
xlim([0, 120])
title('x4')
nexttile
plot(t, X(:,5), 'color', '#3D9BE1'), grid on
xlim([0, 120])
title('x5')
%title(tL2, 'Zoomed-in')
xlabel(tL2, 'Time')
ylabel(tL2, 'Population')
%% Dynamics of Population Growth
function [dx_dt]= TestFunction(~,x)
% Parameters
s = 0.038;
alpha = 0.02;
gamma = 0.10;
r = 0.03;
dH = 0.0083;
dX = 0.0125;
rho = 0.07;
K = 500;
beta = 0.0005;
theta = 0.03;
eta = 0.015;
muH = 0.015;
muI = 0.08;
lambdaP = 0.05;
lambdaL = 0.043;
UP = 0.20;
deltaP = 0.033;
UL = 0.50;
deltaL = 0.05;
kappa = 0.005;
dx_dt(1) = (s) - ((alpha * x(3) * x(1)) / (1 + gamma * x(1))) - (dH * x(1)) + (r * x(2));
dx_dt(2) = ((alpha * x(3) * x(1)) / (1 + gamma * x(1))) - ((r+dX) * x(2));
dx_dt(3) = ((rho * x(3)) * (1 - (x(3) + x(4)) / K)) - (beta * x(3) * x(5)) - (lambdaP * x(6) * x(3)) - (lambdaL * x(7) * x(3)) - (muH * x(3));
dx_dt(4) = (beta * x(3) * x(5)) - (lambdaP * x(6) * x(4)) - (lambdaL * x(7) * x(4)) - (muI * x(4)) - (kappa * x(5) * x(4));
dx_dt(5) = (theta * x(4)) - (eta * x(5));
dx_dt(6) = (UP) - (deltaP * x(6));
dx_dt(7) = (UL) - (deltaL * x(7));
dx_dt = dx_dt';
end
Dhivyadharshini
2025-9-29
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2025-9-29
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