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In: Advanced Math

In a model of a hypothetical chemical oscillator, the dimensionless concentrations x, y>=0 evolve over time...

In a model of a hypothetical chemical oscillator, the dimensionless concentrations x, y>=0 evolve over time according to
dy /dx=1-(b+1)x+ax^2y
dx/dy=bx-ax^2y
where a, b>0 are parameters
a) Find all the fixed points, and perform their linear stability analysis.
b) Show that a Hopf bifurcation occurs at some parameter value b=b_c where b_c is to be determined.

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Expert Solution

Colby Messinger answered 2 years ago
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