We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its...We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）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.展开更多
基金partially supported by a MINECO-FEDER(Grant No.MTM2016-77278-P)a MINECO(Grant No.MTM2013-40998-P)+1 种基金an AGAUR(Grant No.2014SGR-568)partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）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.
