By use of Melnikov function method,the chaos condition and judging criterion of the system under the condition of Smale horseshoe map were given.

Melnikov functions of planar near-Hamiltonian systems and their Hopf bifurcations;

For researching chaotic oscillation in large scale interference power system and enhancing its security,a method to calculate Melnikov was propsed,which analyzed heteroclinic bifurcation of oscillation in nonlinera three-parameter two-generator power system and inferred the condition that Melnikov function have simple zero result.

The critical relations between the base excitation amplitude or the mean fluid flow-rate and the base excitation frequency are obtained by solving Melnikov functions for the distance between stable and unstable manifolds of saddle points of the perturbed system.

Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation.

Melnikov method is an effectively mathematical method which is usually used to prove the existence of chaos in the sense of Smale horseshoes.

Using the Melnikov method, the system s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained.

By using the stochastic nonlinear dynamics theory, based on the stochastic Melnikov method and rate of phase space flux theory, the dynamical stability of ships in random ocean wave and the method on reducing its capsizal are studied.