3 Find the equilibria of the system x 1 2 cosx and analyze

3. Find the equilibria of the system x = 1 - 2 cos(x), and analyze their stabillity.

Solution

equilibrium of system x\' = 1-2cosx

We need to put derivative part = 0

that means x\' =0

=> 1-2cosx = 0

=> cosx = 1/2

x= (6n-1)*pi/3 and x= (6n+1)*pi/3

We got infinte solutions for this equilibria

then we can say that This is not stable

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I hope this will help you!!!