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

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Advance Math

In a model of a hypothetical chemical oscillator, thedimensionless concentrations x, y>=0 evolve over time accordingto
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 stabilityanalysis.
b) Show that a Hopf bifurcation occurs at some parameter valueb=b_c where b_c is to be determined.

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