Bifurcations occur when parameters reach critical values from "summary" of Chaos by James Gleick
Bifurcations are the points at which the behavior of a system changes qualitatively. They mark the transition from order to chaos, or from one kind of order to another. Bifurcations occur when parameters reach critical values. When a system is subjected to a constant input, it may respond in a regular, predictable way. But as a parameter is gradually changed, the system may suddenly switch to an entirely different mode of behavior. The system may bifurcate, splitting into two distinct branches. At a bifurcation point, a small change in a parameter can lead to a large change in the system's behavior. This sensitivity to initial conditions is a hallmark of chaotic systems. In the language of chaos theory, bifurcations are points of instabili...
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