Integrability and limit cycles of the Moon-Rand system

© 2014 Elsevier Ltd. We study the Darboux integrability of the Moon-Rand polynomial differential system. Moreover we study the limit cycles of the perturbed Moon-Rand system bifurcating from the equilibrium point located at the origin, when it is perturbed inside the class of all quadratic polynomial differential systems in R3, and we prove that at first order in the perturbation parameter ε the perturbed system can exhibit one limit cycle, and that at second order it can exhibit four limit cycles bifurcating from the origin. We provide explicit expressions of these limit cycles up to order O(ε2).