Investigation on the Running-In Quality at Different Rotating Speeds by Chaos Theory

Improving running-in quality is an important project of Green Tribology. In actual environment, the running-in quality of mechanical equipment is greatly affected by system parameters. In view of this, running-in experiments were performed at different rotating speeds on a pin-on-disc tribometer. Chaos theory was used to investigate the effect of rotating speeds on the running-in quality. The experimental results showed that the running-in quality could be better evaluated by using the chaotic characteristic parameter “Convergence (CON)”. The greater the CON, the better the running-in quality. With an increase of the rotating speed, CON first gradually increased and then decreased to a certain level, whilst the running-in quality first gradually became better and then became worse. A moderate rotating speed is advantageous to obtain the optimum running-in quality. This contributes to the service life extension and the efficiency improvement, so as to reduce energy consumption.

Dynamical Behaviors of a Pest Epidemic Model with Impulsive Control Over a Patchy Environment

An epidemic model for pest management with impulsive control over a patchy environment is proposed in this paper. We investigate the dynamical behaviors on extinction and permanence and obtain the threshold value [Formula: see text] of dynamics for the impulsive system by utilizing a small amplitude perturbation method, matrix spectral analysis and persistence theory. We prove that the periodic pest-eradication solution of the system is globally asymptotically stable if [Formula: see text], while the system is persistent if [Formula: see text]. Furthermore, by discussion on the two-patch case, we analyze the effects of the dispersal and impulsive control on dynamical behaviors of the system. Some numerical examples are given to illustrate the effectiveness of the obtained results and to demonstrate the complexity such as chaotic characteristic of the system.