Period-doubling bifurcation is a phenomenon observed in dynamical systems where a stable periodic orbit becomes unstable, leading to the emergence of a new periodic orbit with double the period of the original one. This process can occur in various contexts, including mathematical models in science and engineering, and is particularly relevant in the study of nonlinear dynamics and chaos theory.
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A period-doubling bifurcation occurs when a fixed-point multiplier crosses and a nearby period-two orbit is created. Under the generic nondegeneracy conditions, the orbit amplitude is proportional to the square root of the parameter displacement.