Hopf Bifurcation Analysis for a Delayed Business Cycle Model-The Equivalence of Multiple Time Scales Versus Center Manifold Reduction Methods

In this paper, we study the Hopf bifurcation of a model with a second order term, which is the business cycle model with delay. Multiple time scales method, which is mainly used by the engineering researchers, and center manifold reduction method, which is mainly used by researchers from mathematical society, are used to derive the two types of normal forms near the Hopf critical point. A comparison between the two methods shows that the two normal forms are equivalent. Scholars can derive the normal form by choosing appropriate methods according to their actual demands. Moreover, bifurcation analysis and numerical simulations are given to verify the analytical predictions.     

A reliability-based manufacturing process planning method for the components of a complex mechatronic system

Uncertainties in the values of the parameters of a system can originate from the manufacturing tolerances of the system components, which can produce a degree of unreliability in the performance of the system. A systematic framework for realistic reliability assessment of an electro-hydraulic servo system has been presented in this paper with the objective of providing adequate information for the selection of the best manufacturing process for each of the servo valve components. Monte Carlo simulation has been employed to evaluate the effect of these uncertainties of the servo valve parameters on the statistical performance of the system. Possible manufacturing processes have been introduced for each component and the justifiability of using each one has been discussed based on the estimated reliability of the system.     

On the number of limit cycles for a quintic Li\""{e}nard system under polynomial perturbations

In this paper, we mainly study the number of limit cycles for a quintic Li\"{e}nard system under polynomial perturbations. In some cases, we give new estimations for the lower bound of the maximal number of limit cycles.