Partial Extinction, Permanence, and Global Attractivity in Nonautonomousn-Species Gilpin-Ayala Competitive Systems with Impulses

The qualitative properties of general nonautonomousn-species Gilpin-Ayala competitive systems with impulsive effects are studied. Some new criteria on the permanence, extinction, and global attractivity of partial species are established by using the methods of inequalities estimate and Liapunov functions.

Research on Dynamic Friction Compensation of High-Speed Precision Slider

. The tracing precision is greatly influenced because of the friction when high-precise linear motor moved in a low speed.Explore the ways of nonlinear friction compensation in a practical angle. A tribology mathematical model has been found based on the viscoplasticity theory and Stribeck friction mathematical model.This paper aims at applying the Stribeck friction mathematical model to linear motor slider system and designing the controller.The controller can be designed by the feed-forward Integral to conduct identification and compensation online, according to the characters of tribology model.the stability of systems has also been analyzed by using Liapunov functions and LaSalle Invariance Principle.As has been demonstrated by the experimental results, the friction compensation of this model has improved the tracing performance of linear motor slider system.

A note on boundedness of solutions to a class of non-autonomous differential equations of second order

By defining some appropriate Liapunov functions, we discuss boundedness of solutions to a class of non-autonomous and nonlinear differential equations of second order. By this work, we prove some results established in the literature by Liapunov's second method instead of the integral test. We give six examples to illustrate the theoretical analysis in this work and effectiveness of the method utilized here.