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In each of Problems 15 and 16: (a) Find the critical poi

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In each of Problems 15 and 16: (a) Find the critical points. (b) Determine the value of ?, denoted by ?0, where two crit

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In each of Problems 15 and 16: (a) Find the critical points. (b) Determine the value of ?, denoted by ?0, where two critical points coincide. (c) By finding the approximating linear systems and their eigenvalues, determine how the stability properties of these two critical points change as ? passes through the bifurcation point ?0. (d) Draw phase portraits for values of ? near ?0 to show how the transition through the bifurcation point occurs. 15. x? = (3 + x) (1 ? x + y), y? = (y ? 1) (1 + x + ?y); ? > 0

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