[07x08] Solve System of Differential Equations in Julia using DifferentialEquations.jl and Pluto

Learn how to solve a System of Differential Equations in Julia by using the DifferentialEquations.jl package and a Pluto notebook.
As a motivating example, you'll learn how to solve the Lotka-Volterra Equations, also known as the Predator-Prey Equations.
You'll also learn how to build a very sophisticated, interactive Phase Space model that will help you gain intuition regarding the relationship between the predator and prey populations.
Prerequisites:
Knowledge about Differential Equations is not required.
Basic knowledge about Julia Programming Language and Pluto Notebooks is required.
Basic knowledge about how to use the DifferentialEquations.jl package to solve both First Order and Second Order Ordinary Differential Equations is required.
00:00 Intro
01:07 Prerequisites
01:36 Launch Pluto
02:52 Define Problem
12:18 Solve Problem
21:14 Build Interactive Phase Space Model
26:03 Recap
27:38 Outro
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Links for this tutorial
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Code for this tutorial
github.com/julia4ta/tutorials...
Wikipedia Article on Lotka-Volterra Equations
en.wikipedia.org/wiki/Lotka%E...
DifferentialEquations.jl (docs)
diffeq.sciml.ai/stable/
DifferentialEquations.jl (GitHub)
github.com/SciML/Differential...
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Links for this series
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Link to Series 7 Playlist [Julia Differential Equations for Beginners]
• [07x01] How to Install...
The Julia Programming Language
julialang.org/
docs.julialang.org/en/v1/
/ thejulialanguage
DifferentialEquations.jl
diffeq.sciml.ai/stable/
github.com/SciML/Differential...
Pluto.jl (GitHub)
github.com/fonsp/Pluto.jl
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/ @doggodotjl
Thank you!

[@cescalan9]

Bonito recuerdo de ecuaciones que me maravillaron en la juventud, a lápiz y papel, y que vuelven a maravillar en la madurez ahora con JULIA y el gran ingenio didáctico de Doggo: Gracias : )

[@doggodotjl]

¡Sí, es un clásico hecho nuevo otra vez gracias a Julia!

[@cescalan9]

@@doggodotjl Estuve mirando un libro de pregrado, ... debo corregir. No creo que yo haya abordado este problema de sistema de ec. no lineales "a lápiz y papel"... Me traicionó la memoria. Más mérito para los cálculos numéricos. Gracias.

[@sun1908]

Thank you.. This is excellent !!!

[@doggodotjl]

You're welcome!

[@oumardiallo7292]

Another great tutorial. Is the SEIR model in the list of examples to come? Anyway, this is a good start to get there. Thank you!

[@doggodotjl]

I wasn't planning on covering SEIR this series, but I'll put it on my "to-do" list. The next tutorial covers the Lorenz System, which is a System with 3 Ordinary Differential Equations. As far as I understand it, SEIR is a System with 4 Ordinary Differential Equations, so the workflow for solving it should be similar. I'll take a look at it and I'll let you know what I find out!

[@doggodotjl]

Oumar, I put together a Pluto notebook for the SEIR model: github.com/julia4ta/tutorials/tree/master/Series%2007/Files I probably won't be making a tutorial on this subject since I have too many questions about it, but this Pluto notebook does contain a working model, so you can use it as a framework to build your own custom model so you won't have to start from scratch. Let me know if you have any questions. Good luck!

[@oumardiallo7292]

@@doggodotjl I can't thank you enough. Just Amazing for you to share this.Downloaded it and everything run just fine. Merci, merci !!!

[@doggodotjl]

@@oumardiallo7292 It was my pleasure! Thank you for all of your support since the beginning!