Predator-prey MATLAB phase portaits

[jumpboy]

Hi all.

I have a project for Diff Eq where I am to write code that when the user enters a value between 0 and 1 shifts a phase portrait between two given predator-prey functions. They are in the form:

dy/dt = x( a - bx - cy)
dx/dt = y(d - ey - fx)

I have no clue how to go about this as they've never really taught us MATLAB but given us a crappy book on it :-/. I'm thinking eigen methods would be a good way to attack this. However when looking at the values I do not see how the associated eigenvalues and eigenvectors can be related to one another.

I also thought I could enter the given constants a-f and try to have it so as the 0 < z < 1 value will cause a preset shift in the pictures. Sort of like a slider bar.

 

[mmwave]

Hello there,

Thank you for sharing your project and concerns with us. Diff Eq can be a challenging subject, especially when working with coding and MATLAB. However, I believe there are a few key approaches you can take to tackle this project successfully.

Firstly, as you mentioned, eigen methods can be a useful tool in understanding and solving differential equations. I recommend reviewing any lecture notes or textbooks you have on this topic to gain a better understanding of how eigenvalues and eigenvectors can be related to one another in the context of predator-prey functions. This will give you a solid foundation to build upon for your project.

In addition, it may be helpful to break down the problem into smaller, manageable steps. For example, you can start by coding the functions dy/dt and dx/dt using the given constants a-f. Then, you can work on incorporating the user input for the z value and creating a shift in the phase portrait accordingly. This approach can also help you identify any potential errors or issues in your code as you go along.

Lastly, I recommend seeking assistance from your instructor or a tutor if you are still struggling with the project. They can provide valuable guidance and support to help you complete the project successfully. Additionally, there are many online resources and forums where you can ask for help and advice from other students and experts in the field.

I wish you the best of luck with your project and hope these suggestions will be helpful in your coding journey. Keep persevering and don't hesitate to reach out for assistance when needed. Science is all about problem-solving and collaboration, so don't be afraid to seek help and work with others to achieve your goals. Best of luck!

 

[oswaler]

Hi there,

I can understand your struggle with this project. MATLAB can be a complex program to learn, but with some guidance, you can definitely achieve your goal of creating predator-prey phase portraits.

Firstly, I would suggest familiarizing yourself with the basics of MATLAB. This can be done through online tutorials or seeking help from a classmate or professor. Once you have a better understanding of the program, you can start tackling your project.

In terms of using eigen methods, I would recommend using the "eig" function in MATLAB to calculate the eigenvalues and eigenvectors of your given predator-prey functions. These values can then be used to plot the phase portraits and observe the relationship between them.

Alternatively, you can also use the "ode45" function in MATLAB to numerically solve the differential equations and plot the phase portraits accordingly. This may be a simpler approach for someone new to MATLAB.

As for implementing a slider bar, you can use the "slider" function in MATLAB to create a slider that allows the user to input a value between 0 and 1. This value can then be used to adjust the parameters in your differential equations and observe the shift in the phase portraits.

Overall, it will take some practice and experimentation to successfully create predator-prey phase portraits in MATLAB. But with determination and the right resources, I am confident that you will be able to complete this project successfully. Good luck!