On existence of homoclinic orbits for some types of autonomous quadratic systems of differential equations

摘要

The new existence conditions of homoclinic orbits for the system of ordinary quadratic differential equations are founded. Further, the realization of these conditions together with the Shilnikov Homoclinic Theorem guarantees the existence of a chaotic attractor at 3D autonomous quadratic system. Examples of the chaotic attractors are given.