- #1
verd
- 146
- 0
Hi,
So I keep making mistakes trying to find all of the equilibrium points of different simple nonlinear systems. These problems aren't difficult, it's just that I keep taking different approaches to finding the equilibrium points.
Is there a methodological way to know that I have found all of the equilibrium points for a system?
I have a few examples (below)
Example 1:
[tex]\dot{x}=x(3-x-2y)[/tex]
[tex]\dot{y}=y(2-x-y)[/tex]
Example 2:
[tex]\dot{x}=x^2-y[/tex]
[tex]\dot{y}=x-y[/tex]
Example 3:
[tex]\dot{x}=x(2-x-y)[/tex]
[tex]\dot{y}=x-y[/tex]
Example 4:
[tex]\dot{x}=x-y[/tex]
[tex]\dot{y}=1-e^{x}[/tex]
PS, this isn't homework. This is a component of an exam I need to pass, and I'm just looking for a structured way to approach this type of problem.
Thanks in advance
-H
So I keep making mistakes trying to find all of the equilibrium points of different simple nonlinear systems. These problems aren't difficult, it's just that I keep taking different approaches to finding the equilibrium points.
Is there a methodological way to know that I have found all of the equilibrium points for a system?
I have a few examples (below)
Example 1:
[tex]\dot{x}=x(3-x-2y)[/tex]
[tex]\dot{y}=y(2-x-y)[/tex]
Example 2:
[tex]\dot{x}=x^2-y[/tex]
[tex]\dot{y}=x-y[/tex]
Example 3:
[tex]\dot{x}=x(2-x-y)[/tex]
[tex]\dot{y}=x-y[/tex]
Example 4:
[tex]\dot{x}=x-y[/tex]
[tex]\dot{y}=1-e^{x}[/tex]
PS, this isn't homework. This is a component of an exam I need to pass, and I'm just looking for a structured way to approach this type of problem.
Thanks in advance
-H