Estimations of Bounds for the Laser-Plasma Interaction System

To estimate the ultimate bound and positively invariant set of a dynamic system is an important but quite challenging task. This paper is concerned with the ultimate bounds and positively invariant sets for a system describing the laser-plasma interaction. Based on generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive some new ellipsoidal estimates of the globally exponentially attractive set and positively invariant set of the laser-plasma interaction system via the generalized Lyapunov function theory. Furthermore, the estimations derived here contain the existing relative results on the globally exponentially attractive set as special cases and can lead to a series of new estimations.