The construction of homoclinic and heteroclinic orbit in two-dimentsional nonlinear systems based on the quasi-Pade approximation

The conventional quasi-Pad\'e approximants aredeveloped to study the homoclinic and heteroclinic solutions in nonlineardynamic system, and in the solution process in which the disturbanceparameters of system don't be restricted in advance. Firstly, the systemwith cubic nonlinear oscillators is considered. The value ranges of itsparameters can be determined when the homoclinic and heteroclinic orbits areoccurred. Respectively suppose the general formulations homoclinic andheteroclinic solutions which reflect the parameters of the systemdirectly.Meanwhile, the homoclinic and heteroclinic solutions ofthe strongly nonlinear autonomous system are derived successfully. Secondly,the periodic solutions of the non-autonomous system are derived under thedirect consideration of the disturbance parameters, which are satisfied theconditions of the homoclinic and heteroclinic solutions. Finally, twoheteroclinic solutions functions are constructed in order to reduce thecomputational complexity. The validity and accuracy of the quasi-Pad\'eapproximants are proved by comparing with the numerical computation.