Answer: BifurcationsThe term bifurcation generally refers to something splitting apart
Chapter 6, Problem 34(choose chapter or problem)
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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