# Van der pol Equation Simulation in Simulink

• engineer_stud
In summary, the conversation is about implementing two differential equations into Simulink and using different blocks to create a system. The equations involve a parameter mu and the goal is to plot the variables x1 and x2 against each other in a simulation. The user has successfully set up the model in Simulink and is now trying to run it from a MATLAB script, but is encountering a problem where no graph is being displayed.
engineer_stud

## Homework Statement

As the title says, I am trying to implement two differential equations into Simulink. I don't know how to start. How do I know what to start with, which block goes where? when do I add something and when do I know to subtract something using the sum block. When I got my model ready, how do I know what I have done is right?

The system should be realized using the following blocks :

Integrator, sum, product, gain and To Workspace.

## Homework Equations

Code:
\begin{align}
\dot{x_{1}}=x_{2}\\
\dot{x_{2}}=-x_{1}+\mu(1-x^{2}_{1})x_{2}
\end{align}

where
Code:
\mu>0

## The Attempt at a Solution

Alright boys, thank you for the help on the Simulink part (NOT). I have now managed to set up the model in simulink. Now I am suppose to run the model from a MATLAB M-file (script). I initialize the variables and run the simulation from the script, plotting x1 and x2 against each other.

The problem is that I don't get any graph? Just an empty figure.

mu = 5;
t_sim = 10;
x_10 = 1;
x_20 = 2;

sim('vanderpol');

time1 = x1.time;
x1 = x1.signals.values;

time2 = x2.time;
x2 = x2.signals.values;

figure(1);
grid on;
plot(x1,x2);

## 1. What is a Van der Pol equation?

The Van der Pol equation is a second-order nonlinear differential equation that describes the behavior of a damped oscillator. It was first introduced by Dutch physicist Balthasar van der Pol in the 1920s and has been widely used in various fields of science and engineering.

## 2. How is the Van der Pol equation simulated in Simulink?

The Van der Pol equation can be simulated in Simulink by using the "ode45" solver and setting the equation as the input function. This solver uses a Runge-Kutta method to numerically solve the equation and provide a graphical output of the simulation.

## 3. What are the key components of a Van der Pol equation simulation in Simulink?

The key components of a Van der Pol equation simulation in Simulink include the "ode45" solver, the input function representing the equation, and a graphical output that shows the behavior of the damped oscillator over time.

## 4. How can the parameters of the Van der Pol equation be adjusted in Simulink?

The parameters of the Van der Pol equation, such as the damping coefficient and the nonlinearity coefficient, can be adjusted in Simulink by using the "Constant" block and connecting it to the appropriate input in the equation. This allows for the simulation of different scenarios and analysis of the system's behavior.

## 5. What are the applications of simulating the Van der Pol equation in Simulink?

The simulation of the Van der Pol equation in Simulink has various applications in fields such as physics, engineering, and biology. It can be used to model and analyze the behavior of electrical circuits, chemical reactions, and biological systems. It is also commonly used in control systems and signal processing.

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