Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...

Using a fixed point theorem of strict-set-contraction, we prove the existence of positive periodic solutions for a class of nonautonomous impulsive neutral functional differential system with time-varying delays on time scales.

In this paper, we consider a nonautonomous multispecies competition predator-prey system with Holling’s type III functional response and prey supplement. It is proved that the system is uniformly persistent under some conditions. Furthermore, we show that the system has a unique positive periodic solution which is globally asymptotically stable.

background: cigarette smoking is one of the most important health‑related risk factors in terms of morbidity and mortality. in this study, we introduced a new method for deriving the transitional probabilities of smoking stages from a cross‑sectional study and simulated a long‑term smoking behavior for adolescents. methods: in this study in 2010, a total of 4853 high school students were random...

We generalize a criterion of Yakubovich for the absolute stability of control processes with periodic coefficients to the case when the coefficients are bounded and uniformly continuous functions. 1. Introduction. In the past two decades, the study of differential equations with time-varying coefficients (nonautonomous differential equations) has benefited from the use of methods of the ergodic...

We present Lyapunov stability and asymptotic theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete delays, which may be nonautonomous the result, but autonomous (or periodically forced) result. main technique is replace DDE by a ordinary equation (ODE) where delayed t...