Publications

BibTex format

@article{Doan:2018:1361-6544/aad208,
author = {Doan, TS and Engel, M and Lamb, J and Rasmussen, M},
doi = {1361-6544/aad208},
journal = {Nonlinearity},
title = {Hopf bifurcation with additive noise},
url = {http://dx.doi.org/10.1088/1361-6544/aad208},
volume = {31},
year = {2018}
}

Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II) a random attractor with non-uniform synchronisation of trajectories and (III) a random attractor without synchronisation of trajectories. The random attractors in phases (I) and (II) are random equilibrium points with negative Lyapunov exponents while in phase (III) there is a so-called random strange attractor with positive Lyapunov exponent.We analyse the occurrence of the different dynamical phases as a function of the linear stability of the origin (deterministic Hopf bifurcation parameter) and shear (amplitude-phase coupling parameter). We show that small shear implies synchronisation and obtain that synchronisation cannot be uniform in the absence of linear stability at the origin or in the presence of sufficiently strong shear. We provide numerical results in support of a conjecture that irrespective of the linear stability of the origin, there is a critical strength of the shear at which the system dynamics loses synchronisation and enters phase (III).
AU  - Doan,TS
AU  - Engel,M
AU  - Lamb,J
AU  - Rasmussen,M
DO  - 1361-6544/aad208
PY  - 2018///
SN  - 0951-7715
TI  - Hopf bifurcation with additive noise
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/1361-6544/aad208
UR  - http://hdl.handle.net/10044/1/62264
VL  - 31
ER  -

Download

ProfessorJeroenLamb

Contact

Location

Summary

Citation

BibTex format

RIS format (EndNote, RefMan)