Normal form analysis of stochastically forced dynamical systems
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The possibility of reducing the dynamics of a system undergoing a Hopf bifurcation and forced by multiplicative noise to a universal normal form is examined on a simple model of geophysical interest. It is shown that the normal form equations and the stationary probability distribution depend on the way the noise is coupled to the original system. The universality of the normal forms is thus severely limited in the presence of noise.
CitationNicolis, C.; Nicolis, G. (1986). Normal form analysis of stochastically forced dynamical systems. , Dynamics and Stability of Systems, Vol. 1, Issue 3, 249-253, DOI: 10.1080/02681118608806017.