The Lower Bounds of T-Periodic Solutions for the Forced Duffing Equation

Nonresonant Excitation of the Forced Duffing Equation

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

Existence of Periodic Solutions for the Duffing Equation with Impulses

Lower Bounds for the stability Degree of periodic solutions in forced nonlinear Systems

In this paper the problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. Some lower bounds for the degree of local exponential stability of a given periodic solution are provided by mixing results concerning the analysis of linear time varying systems and the real parametric stability margin of uncertain linear time invariant syst...

Classification of solutions of the forced periodic nonlinear Schrödinger equation

The integrable structure of the periodic one-dimensional nonlinear Schrödinger equation is utilized to gain insights regarding the perturbed near-integrable dynamics. After recalling the known results regarding the structure and stability of the unperturbed standing and travelling waves solutions, two new stability results are presented: (1) it is shown numerically that the stability of the ‘ou...

Counting periodic solutions of the forced pendulum equation

Let h be a holomorphic function with h(0) = 1. The number of zeros of h on a disk centered at the origin can be controlled by the maximum value of |h| on a larger disk. This is a classical result in complex analysis that is sometimes called Jensen’s inequality (see for instance [4]). In [2] Il’yashenko and Yakovenko applied this result together with the theory of conformal mappings to count the...