Llibre, Jaume et Valls, Claudia, On the Darboux integrability of the Hindmarsh.Rose burster, Acta mathematica Sinica. English series (Print) , 34(6), 2018, pp. 947-958
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.=.(s(x.x0).z), where b, I, ., 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.