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Published on: May 29, 2014
Isostables for Stochastic Oscillators
Alberto Pérez-Cervera1, Benjamin Lindner2, Peter J Thomas3
1National Research University Higher School of Economics, 109208 Moscow, Russia and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Abstract:
Thomas and Lindner [P. J. Thomas and B. Lindner, Phys. Rev. Lett. 113, 254101 (2014).PRLTAO0031-900710.1103/PhysRevLett.113.254101], defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward Kolmogorov (or stochastic Koopman) operator. We complete the phase-amplitude description of noisy oscillators by defining the stochastic isostable coordinate as the eigenfunction with the least negative nontrivial real eigenvalue. Our results suggest a framework for stochastic limit cycle dynamics that encompasses noise-induced oscillations.
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