Citation: |
[1] |
L. Arnold, "Random Dynamical Systems," Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. |
[2] |
L. Arnold, G. Bleckert and K. R. Schenk-Hoppé, The stochastic Brusselator: Parametric noise destroys Hopf bifurcation, in "Stochastic Dynamics" (Bremen, 1997), 71-92, Springer, New York, 1999. |
[3] |
L. Arnold, N. Sri Namachchivaya and K. R. Schenk-Hoppé, Toward an understanding of stochastic Hopf bifurcation: A case study, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 6 (1996), 1947-1975.doi: 10.1142/S0218127496001272. |
[4] |
I. Bashkirtseva, L. Ryashko and H. Schurz, Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances, Chaos Solitons Fractals, 39 (2009), 72-82.doi: 10.1016/j.chaos.2007.01.128. |
[5] |
F. Colonius and W. Kliemann, Topological, smooth, and control techniques for perturbed systems, in "Stochastic Dynamics" (Bremen, 1997) (eds. H. Crauel and M. Gundlach), Springer, New York, (1999), 181-208. |
[6] |
F. Colonius and W. Kliemann, "The Dynamics of Control," With an appendix by Lars Grüne, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2000. |
[7] |
J. L. Doob, "Stochastic Processes," John Wiley & Sons, Inc., New York, Chapman & Hall, Limited, London, 1953. |
[8] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields," Applied Mathematical Sciences, 42, Springer-Verlag, New York, 1983, revised 1990. |
[9] |
A. J. Homburg and T. Young, Hard bifurcations in dynamical systems with bounded random perturbations, Regular & Chaotic Dynamics, 11 (2006), 247-258.doi: 10.1070/RD2006v011n02ABEH000348. |
[10] |
A. J. Homburg and T. Young, Bifurcations for random differential equations with bounded noise on surfaces, Topol. Methods Nonlinear Anal., 35 (2010), 77-97. |
[11] |
R. A. Johnson, Some questions in random dynamical systems involving real noise processes, in "Stochastic Dynamics" (Bremen, 1997) (eds. H. Crauel and M. Gundlach), Springer, New York, (1999), 147-180. |
[12] |
Yu. A. Kuznetsov, "Elements of Applied Bifurcation Theory," Applied Mathematical Sciences, 112, Springer Verlag, New York, 1995. |
[13] |
S. Wieczorek, Stochastic bifurcation in noise-driven lasers and Hopf oscillators, Phys. Rev. E (3), 79 (2009), 036209, 10 pp. |
[14] |
H. Zmarrou and A. J. Homburg, Bifurcations of stationary measures of random diffeomorphisms, Ergod. Th. Dyn. Systems, 27 (2007), 1651-1692. |