# Doing a phase-space portrait in matlab

• MATLAB
• bagram
In summary, the conversation is about a system of equations involving matrices and trigonometric functions, and the challenge of plotting it in MATLAB as a phase-space portrait. The suggested approach is to compute the derivatives at t=0 and plot them using the quiver() function. The individual has tried several methods but has not been successful. Further clarification is needed on whether completing the derivative at t=0 is the same as n=0.

#### bagram

So I have this system of equations:

$$\binom{x_{n+1}}{y_{n+1}}=\begin{pmatrix}e^{r} & 0 \\ 0 & e^{-r} \end{pmatrix}\begin{pmatrix}cos(\phi+I_{n}) & -sin(\phi+I_{n}) \\ sin(\phi+I_{n}) & cos(\phi+I_{n}) \end{pmatrix}\begin{pmatrix}x_{n}\\ y_{n} \end{pmatrix}$$

where
$$I_{n}=x_{n}^2+y_{n}^2$$

I have no idea how to plot that in MATLAB as a phase-space portrait...

Any help would be great

What have you tried?

In general you would compute the derivatives at t=0 on a grid, then plot them as a vector field using the quiver() function.

i've tried, generating a set and points and just sketching it and tried using the ezsurf/surf function to do it... but both ways failed. Does completing the derivative at t=0 the same as n=0?

## 1. What is a phase-space portrait?

A phase-space portrait is a graphical representation of the behavior of a system in terms of its state variables, typically position and velocity. It shows the trajectory of the system in its phase space, which is a mathematical representation of all possible states of the system.

## 2. How do I create a phase-space portrait in Matlab?

To create a phase-space portrait in Matlab, you can use the built-in function "quiver" to plot the velocity vectors of the system at different points in its phase space. You can also use the "plot" function to plot the trajectory of the system based on its state variables.

## 3. What are the benefits of using a phase-space portrait?

A phase-space portrait allows you to visualize and analyze the behavior of a system over time, which can help you understand its dynamics and make predictions about its future behavior. It also allows you to identify any critical points or regions of instability in the system.

## 4. How can I interpret a phase-space portrait?

In a phase-space portrait, the position and direction of the arrows represent the velocity of the system at a particular point in its phase space. The trajectory of the system can also give you information about its stability and any potential oscillations or cycles.

## 5. Can I use a phase-space portrait to study any type of system?

Yes, a phase-space portrait can be used to study a wide range of systems, including physical systems, chemical reactions, and biological systems. However, the type of phase space and the equations used to generate the portrait may vary depending on the specific system and its behavior.