x'=ax +by -x (x + 2y ) y'=-bx +ay -y (x + 2y) 4) Consider the...

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x'=ax +by -x (x + 2y ) y'=-bx +ay -y (x² + 2y²) 4) Consider the system a) Prove that for each a <0, there are no non-trivial periodic solutions. b) Prove that for each a>0, there exists a non-trivial periodic solution. c) Considering a as a bifurcation parameter, what kind of bifurcation occurs and at what value of a? x'=ax +by -x (x + 2y ) y'=-bx +ay -y (x² + 2y²) 4) Consider the system a) Prove that for each a <0, there are no non-trivial periodic solutions. b) Prove that for each a>0, there exists a non-trivial periodic solution. c) Considering a as a bifurcation parameter, what kind of bifurcation occurs and at what value of a?