Synchronization theory for forced oscillations in second-order systems

Synchronization Theory for Forced Oscillations in Second-Order Systems ~

We consider differential equations of the form ~ + ~f(x, ~ ) + x = Eu, where E > 0 is supposed to be small. For piecewise continuous controls u(t), satisfying lu( t ) l -1 , we present sulIicient conditions for the existence of 2¢r-periodic solutions with a given amplitude. We present a method for determining the limiting behavior of controls fi, for which the equation has a 27r-periodic soluti...

BRANCHES OF FORCED OSCILLATIONS IN DEGENERATE SYSTEMS OF SECOND ORDER ODEs

This paper is devoted to studying the set of oscillations of a mass point, constrained to a smooth manifold, and forced by an autonomous vector field G with a periodic perturbation F . We focus on a class of systems where G is “degenerate”: its set of zeros being a noncompact submanifold of the constraint. There seem to be no results in the literature for this general case while the “extreme” c...

Finite Time Mix Synchronization of Delay Fractional-Order Chaotic Systems

Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...

Waveform Design using Second Order Cone Programming in Radar Systems

Transmit waveform design is one of the most important problems in active sensing and communication systems. This problem, due to the complexity and non-convexity, has been always the main topic of many papers for the decades. However, still an optimal solution which guarantees a global minimum for this multi-variable optimization problem is not found. In this paper, we propose an attracting met...

Bifurcation and Synchronization in Parametrically Forced Systems