Journal
PHYSICAL REVIEW E
Volume 64, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.64.056219
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A different method to detect the stochastic bifurcation point of a one-dimensional mapping in the presence of noise is proposed. This method analyzes the eigenvalues and eigenfunctions of the noisy Frobenius-Perron operator. The invariant density or the eigenfunction of the eigenvalue I of the operator possesses static information of the noisy one-dimensional dynamics while the other eigenvalues and eigenfunctions have dynamic information. Clear bifurcation phenomena have been observed in a noisy sine-circle map and both stochastic saddle-node and period-doubling bifurcation points have been successfully defined in terms of the eigenvalues.
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