The Method for Solving Homoclinic/Heteroclinic Orbits‐ The Undetermined Coefficient Method and its applications for a New Chaotic System Available to Purchase

A lot of chaotic motions in nonlinear dynamical systems take place arising from the homoclinic/heteroclinic intersections. However, it is difficult to solve the homoclinic or heteroclinic orbits in most nonlinear dynamical systems. One method for solving the homoclinic/heteroclinic orbits of nonlinear dynamical systems, named undetermined coefficient method, is presented in this paper. With this method, the series expansion of the heteroclinic orbit for a new nonlinear system are obtained. It analytically demonstrates that there exists one heteroclinic orbit of the Si’lnikov type that connects the two equilibrium points, therefore Smale horseshoe chaos may occur for this system via the Sil’nikov criterion.