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- Title
On the Darboux integrability of the Hindmarsh-Rose burster.
- Authors
Llibre, Jaume; Valls, Clàudia
- Abstract
We study the Hindmarsh-Rose burster which can be described by the differential system x˙=y−x3+bx2+I−z,y˙=1−5x2−y,z˙=μ(s(x−x0)−z),<graphic></graphic> where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
- Subjects
DARBOUX transformations; EXTERIOR differential systems; POLYNOMIALS; EXPONENTIAL functions; DIFFERENTIAL invariants
- Publication
Acta Mathematica Sinica, 2018, Vol 34, Issue 6, p947
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-017-5661-1