Consider the one parameter family of linear systems given by (78) = (1-5-²ª) (1), a where x(t) and y(t) are real-value f

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Consider The One Parameter Family Of Linear Systems Given By 78 1 5 A 1 A Where X T And Y T Are Real Value F 1 (65.63 KiB) Viewed 10 times

Consider the one parameter family of linear systems given by (78) = (1-5-²ª) (1), a where x(t) and y(t) are real-value functions of t, and a € R is a parameter. (a) Determine all values of a at which bifurcations take place. (Hint: Recall that a bifurcation occurs when there is a change in the qualitative behavior of the solution.) [4 marks] (b) Demonstrate your result in part (a) graphically by drawing the rele- vant curve in the trace-determinant plane. [4 marks] (c) For each of the bifurcation you found in part (a), illustrate the sys- tem's behavior before and after the bifurcation by showing and very briefly discussing the relevant phase portraits. [4 marks]