In this paper we investigate a non-linear and non-local one dimensional transport equation under random perturbations on the real line. We first establish local-in-time theory, i.e., existence, uniqueness blow-up criterion for pathwise solutions in Sobolev spaces Hs with s>3. Thereafter, give picture of long time behavior based type noise consider. On hand, identify family noises such that can ...

The neuron state modeling and the local field modeling provides two fundamental modeling approaches to neural network research, based on which a neural network system can be called either as a static neural network model or as a local field neural network model. These two models are theoretically compared in terms of their trajectory transformation property, equilibrium correspondence property,...

A two-step controller synthesis method is proposed in this paper for a class of uncertain nonlinear systems described by piecewise affine differential inclusions. In the first step, a robust linear controller is designed for the linear differential inclusion that describes the dynamics of the nonlinear system close to the equilibrium point. In the second step, a stabilizing piecewise affine con...

Recently, geometrically thick disks around black holes have been studied by many authors. I) These models may exist in the inner region of accretion disks and explain the generation of high luminosity and colliminated jets in quasers and active galactic nuclei. In such tori, there is no reason for the rotation law to be Keplerian as pressure force plays a role in the equilibrium structure. Thes...

The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number [Formula: see text] is investigated...

The simplification resulting from reduction of dimension involved in the study of invariant manifolds of differential equations is often difficult to achieve in practice. Appropriate coordinate systems are difficult to find or are essentially local in nature thus complicating analysis of global dynamics. This paper develops an approach which avoids the selection of coordinate systems on the man...