Answer: BifurcationsThe term bifurcation generally refers to something splitting apart

Chapter 6, Problem 34

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BifurcationsThe term bifurcation generally refers to something splitting apart. With regard to differential equations or systems involving a parameter, it refers to abrupt changes in the character of the solutions as the parameter is changed continuously. 33 through 36 illustrate sensitive cases in which small perturbations in the coefcients of a linear or almost linear system can change the type or stability (or both) of a critical point.Consider the linear systemdx dt D! x C*y;dy dt D x !y:Show that the critical point .0;0/ is (a) a stable spiral point if *<0 ; (b) a stable node if0 5 *<1. Thus small perturbations of the system x0D!x, y0Dx!y can change the type of the critical point .0;0/ without changing its stability.

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