Question: no missing data, images or graphs. Please provide the explanation. Consider :'c = m 90 cos ac. 1- Verify that X (t) := :c(t) satises

no missing data, images or graphs. Please provide the explanation.

Consider :'c = m 90 cos ac. 1- Verify that X (t) := :c(t) satises the same ODE. 2. Use the Taylor expansion to show that there is a pitchfork bifurcation at 35* = 0. Find the bifurcation point To. Is it supercritical or subcritical? 3- It is clear that when 7' = 0, a: = g is a xed-point. Calculate its characteristic time scale

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