Revealing asymmetric homoclinic and heteroclinic orbits

Although scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in symmetric Lorenz, Chen, and Lü systems, they have rarely dealt with asymmetric ones of the corresponding asymmetric analogues, to the best of our knowledge. To clarify this subject, this work revisited an asymmetric Chen system and reveals a single/a pair of asymmetric heteroclinic/homoclinic orbits, which are justified with numerical experiments.