A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromymatrix of the closed-loop system, we obtain conditions under whi...

Some classical types of nonlinear periodic wave motion are studied in special coordinates. In the case of cylinder coordinates, the usual perturbation techniques leads to the overdetermined systems of linear algebraic equations for unknown coefficients whose compatibility is key step of the investigation. Their solutions give solutions to the nonlinear wave equation which are periodic in time a...

An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for superharmonic resonances of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniq...

To solving nonlinear control problems and especially nonlinear optimal control problems (NOCP), classical methods are not usually efficient. In this paper we introduce a new approach for solving this class of problems by using Nonlinear Programming Problem (NLPP). First, we transfer the original problem to a new problem in form of calculus of variations. Then we discretize the new problem and s...

Experimental and numerical investigations are carried out on an autoparametric system consisting of a composite pendulum attached to a harmonically base excited mass-spring subsystem. The dynamic behavior of such a mechanical system is governedby a set of coupled nonlinear equations with periodic parameters. Particular attention is paid to the dynamic behavior of the pendulum. The periodic doub...

In this paper, we formulate a robust SEIR epidemic disease model with a profitless delay and nonlinear incidence, and analyze the dynamics behaviors of the model under pulse vaccination. By use of the discrete dynamical system determined by the stroboscopic map, we obtain an ’infection-free’ periodic solution, further, show that the ’infection-free’ periodic solution is globally attractive when...

‎in this paper‎, ‎we investigate a damped korteweg-de‎ ‎vries equation with forcing on a periodic domain‎ ‎$mathbb{t}=mathbb{r}/(2pimathbb{z})$‎. ‎we can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

...