Synchronous Perturbation at the Origin and Equator in a Septic Vector Field

In this paper, the problem of bifurcation of limit cycles from the origin and equator in a class of septic polynomial differential system is investigated. Using the computer algebra system-MATHEMATICA, the limit cycle configurations of {(8), 3} and {(3), 6} are obtained under synchronous perturbation at the origin and equator. To our knowledge, up to now, this is the first time that the problem of limit cycles bifurcated from the origin and equator under synchronous perturbed conditions in a septic system is investigated.