Abstract
A stochastic Poincaré-Bendixson theorem and its generalized theorem are given in this paper. The aim of these theorems is to show the existence of a crater-like stationary distribution for a stochastic planar autonomous system. The main theorems are applied on a stochastic predator-prey system as an instruction. For example, stochastic Hopf bifurcation phenomenon is observed when the qualitative change of the shape of the stationary distribution is taken as an indicator of bifurcation.
| Original language | English |
|---|---|
| Article number | 1350070 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 23 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2013 |
| Externally published | Yes |
Keywords
- Brownian motion
- Crater-like stationary distribution
- Dynkin's formula
- Numerical simulations
- Phenomenological bifurcation
- Stopping time
Fingerprint
Dive into the research topics of 'Stochastic Poincaré-Bendixson theorem and its application on stochastic hopf bifurcation'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver