How do I find the equilibria of this autonomous system of ODEs? x &#x2032; </msup

Davis Osborn

Davis Osborn

Answered question

2022-06-01

How do I find the equilibria of this autonomous system of ODEs?
x ( t ) = x ( x 3 2 y 3 )
y ( t ) = y ( 2 x 3 y 3 )

Answer & Explanation

cheesefagoubyv

cheesefagoubyv

Beginner2022-06-02Added 1 answers

Let u ( x , y ) = x ( x 3 2 y 3 ) and v ( x , y ) = y ( 2 x 3 y 3 ).
- If x = 0 and v ( x , y ) = 0 then y 4 = 0 hence y = 0.<br- If y = 0 and u ( x , y ) = 0 then x 4 = 0 hence x = 0.
- If x 0, y 0 and u ( x , y ) = v ( x , y ) = 0 then x 3 = 2 y 3 and y 3 = 2 x 3 hence x 3 = 4 x 3 , thus x=0 and y = 0.
Finally, the only equilibrium is at ( x , y ) = ( 0 , 0 ).
Jabari Pitts

Jabari Pitts

Beginner2022-06-03Added 2 answers

Finally, now I can solve my problem with my numbers, thanks!

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