Noisy heteroclinic networks

Springer Science and Business Media LLC - Tập 150 Số 1-2 - Trang 1-42 - 2011
Yuri Bakhtin1
1School of Mathematics, Georgia Tech, Atlanta GA, 30332-0160, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Armbruster D., Stone E., Kirk V.: Noisy heteroclinic networks. Chaos 13(1), 71–86 (2003)

Bakhtin Y.: Exit asymptotics for small diffusion about an unstable equilibrium. Stoch. Process. Appl. 118(5), 839–851 (2008)

Billingsley, P.: Convergence of probability measures. In: Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edn. Wiley, New York (1999). A Wiley-Interscience Publication

Blagoveščenskiĭ J.N.: Diffusion processes depending on a small parameter. Teor. Verojatnost. i Primenen. 7, 135–152 (1962)

Freidlin, M.I., Wentzell, A.D.: Random perturbations of dynamical systems. In: Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 260, 2nd edn. Springer, New York (1998). Translated from the 1979 Russian original by Joseph Szücs

Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus. In: Graduate Texts in Mathematics, vol. 113. Springer, New York (1988)

Katok, A., Hasselblatt, B.: Introduction to the modern theory of dynamical systems. In: Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge University Press, Cambridge (1995). With a supplementary chapter by Katok and Leonardo Mendoza

Kifer Y.: The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point. Israel J. Math. 40(1), 74–96 (1981)

Krupa M.: Robust heteroclinic cycles. J. Nonlinear Sci. 7(2), 129–176 (1997)

Rabinovich M.I., Huerta R., Afraimovich V.: Dynamics of sequential decision making. Phys. Rev. Lett. 97(18), 188103 (2006)

Skorohod A.V.: Limit theorems for stochastic processes. Teor. Veroyatnost. i Primenen. 1, 289–319 (1956)