based on credibilistic value-at-risk (cvar) of regularfuzzy variable, we introduce a new cvar reduction method fortype-2 fuzzy variables. the reduced fuzzy variables arecharacterized by parametric possibility distributions. we establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. the convex properties of second order moments with ...

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

With the advent of high-speed computation and the desire to analyze increasingly complex behavior in power systems, simulation techniques are gaining importance and prevalence. However, while simulations of large, interconnected power systems are feasible, they remain time-consuming. Additionally, the models and parameters used in simulations are uncertain, due to measurement uncertainty, the n...

Complement is an important pathway in innate immunity, inflammation, and many disease processes. However, despite its importance, there are few validated mathematical models of complement activation. In this study, we developed an ensemble of experimentally validated reduced order complement models. We combined ordinary differential equations with logical rules to produce a compact yet predicti...

The use of finite element or finite difference techniques to discretize nonlinear smart material system models can yield full-order numerical models that accurately characterize the system dynamics but do so at significant computational cost. This can preclude the use of these full-order models for uncertainty analysis, sensitivity analysis, system design, or real-time control implementation. I...