[5] [6] [4] 564 4. Draw bifurcation diagrams for the following systems depending on the parameter...

 

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[5] [6] [4] 564 4. Draw bifurcation diagrams for the following systems depending on the parameter a. Indi- cate a standard name for each of the observed bifurcations. (a) x = -9 -2x2 x4 2+x2 - - 2. [4] [6] -X2. (b) x = (x-2a)(x + x 1 +). (c) x= = x r(1+asinh). (d) = (a+a-2)r r, 4=1+r, where r, are polar coordinates. (e) 1 a 1+ cosh x1, x2 = a + a- = [5] [6] [4] 564 4. Draw bifurcation diagrams for the following systems depending on the parameter a. Indi- cate a standard name for each of the observed bifurcations. (a) x = -9 -2x2 x4 2+x2 - - 2. [4] [6] -X2. (b) x = (x-2a)(x + x 1 +). (c) x= = x r(1+asinh). (d) = (a+a-2)r r, 4=1+r, where r, are polar coordinates. (e) 1 a 1+ cosh x1, x2 = a + a- =