Stabilization by noise of a ℂ2-valued coupled system

@article{Chen2016StabilizationBN,
  title={Stabilization by noise of a ℂ2-valued coupled system},
  author={Joe P. J. Chen and Lance Ford and Derek Kielty and Rajeshwari Majumdar and Heather McCain and Dylan O’Connell and Fan Ny Shum},
  journal={Stochastics and Dynamics},
  year={2016},
  volume={17},
  pages={1750046}
}
D. Herzog and J. Mattingly have shown that a ℂ-valued polynomial ODE with finite-time blow-up solutions may be stabilized by the addition of ℂ-valued Brownian noise. In this paper, we extend their results to a ℂ2-valued system of coupled ODEs with finite-time blow-up solutions. We show analytically and numerically that stabilization can be achieved in our setting by adding a suitable Brownian noise, and that the resulting system of SDEs is ergodic. The proof uses the Girsanov theorem to induce… 
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