Back to Search
Start Over
A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . Jan2018, Vol. 28 Issue 1, p1-8. 8p. - Publication Year :
- 2018
-
Abstract
- We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states with its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i)When the non-Gaussianity parameter in Lévy noise varies, there is either one, two or no backward pitchfork type bifurcations; (ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations; (iii) The non- Gaussian Lévy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STOCHASTIC analysis
*BIFURCATION theory
*VECTOR fields
*GAUSSIAN processes
*NOISE
Subjects
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 28
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 128251386
- Full Text :
- https://doi.org/10.1142/S0218127418500177