Question

Simulate Van der Pol Equation The objective is to simulate the Van der Pol equation which came about with electrical circuits with vacuum tubes. Here are the equations: dy dt dv %Simulation Parameter tend-100; % total simulation time seconds % Initial Conditions %Parameters mu 0.2 Generate two figures. Figure 1 a. Title should state: "Van der Pol Equation" Two plots one above the other: b. Top plot is time vs. y Y-axis should have "y" a. c. Middle plot is time vs. v a. Y-axis should have " b. X-axis should have "Time (seconds)" Figure 2 a. Title should state: "Van der Pol Equation Phase Portrait One plot b. Plot y vs v a. Y-axis should have "V" b. X-axis should have y" Paste your figures and code here (both your main program and ode function file).

Answer 1

Function File

function xdot = vdp1(t,x) %Defining Van der Pol equation
xdot = [x(2); 0.2*(1-x(1)^2)*x(2)-x(1)];
end

Script File

%Defining xdot matrix as [ydot vdot] and x matrix as [y v]
%Using ode45 to solve the differential equation
[t,x] = ode45(@vdp1,[0 100],[0.1;0.1]);

%Plotting graph between y and time and v and time
plot(t,x(:,1),'-o',t,x(:,2),'-o')
title('Van der Pol Equation');
xlabel('Time (seconds)');
ylabel('Solution y and v');
legend('y','v')

figure
%Plotting graph between v and y
plot(x(:,1),x(:,2))
title('Van der Pol Equation Phase Portrait');
xlabel('y');
ylabel('v');

Van der Pol Equation 2.5 1.5 0.5 0.5 1.5 -2 -2.5 40 50 Time (seconds) 10 20 30 60 70 90 100

Van der Pol Equation Phase Portrait 2.5 1.5 0.5 0.5 1.5 -2 2.5 0.5 1.5 -2 1.5 -1 0.5