# A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

@article{Kuehn2011AMF, title={A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications}, author={Christian Kuehn}, journal={Journal of Nonlinear Science}, year={2011}, volume={23}, pages={457-510} }

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical…

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