Thread: Systems of differential equations and equilibrium points...

Hi again guys, hope you can help with this simple question...

I am up to systems of differential equations and their resulting equilibrium points.

Now, when faced with finding their equilibrium points, is the a simple way of knowing how many points we will find or are looking for:

I am currently only up to working on two differential equations. The ones am working on are also linear.

I am guessing that because they both only linear, I will have 2x equilibrium points?

Originally Posted by MaverickUK82

Hi again guys, hope you can help with this simple question...

I am up to systems of differential equations and their resulting equilibrium points.

Now, when faced with finding their equilibrium points, is the a simple way of knowing how many points we will find or are looking for:

I am currently only up to working on two differential equations. The ones am working on are also linear.

I am guessing that because they both only linear, I will have 2x equilibrium points?

In general if you have the the system ODE's





This equilibrium points are the solutions to the system of equation



If you have a plane autonomous system the linear system in P and Q will have exactly one solution, and hence one equilibrium point.

A system of linear equation has either a unique solution, an infinite number of solutions, or no solution.

That is, a system of any number of linear differential equations has either a single equilibrium point, an infinite number of equilibrium points (forming a subspace), or none.

That's bad because i've found two equilibrium points for the system I'm working on. Have I explained it correctly.

Originally Posted by MaverickUK82

That's bad because i've found two equilibrium points for the system I'm working on. Have I explained it correctly.

What is the system of ODE's

x'=-axy+bx
y'=cxy-dy


the x' and y' are supposed to be liebniz notation, i.e., an x with a single dot above it but I can't do it in latex...

Originally Posted by MaverickUK82

x'=-axy+bx
y'=cxy-dy


the x' and y' are supposed to be liebniz notation, i.e., an x with a single dot above it but I can't do it in latex...

First off the equations are not linear! You have products of x and y.

you can you \dot for time derivatives



and

and yes there are two critical points