Abstract
We study the Hindmarsh–Rose burster which can be described by the differential system
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.
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The first author is partially supported by a MINECO-FEDER (Grant No. MTM2016-77278-P) a MINECO (Grant No. MTM2013-40998-P) and an AGAUR (Grant No. 2014SGR-568); the second author is partially supported by FCT/Portugal through UID/MAT/04459/2013
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Llibre, J., Valls, C. On the Darboux integrability of the Hindmarsh–Rose burster. Acta. Math. Sin.-English Ser. 34, 947–958 (2018). https://doi.org/10.1007/s10114-017-5661-1
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DOI: https://doi.org/10.1007/s10114-017-5661-1
Keywords
- Polynomial integrability
- rational integrability
- Darboux polynomials
- Darboux first integrals
- invariant algebraic surfaces
- exponential factors
- Hindmarsh–Rose burster