Bifurcation of Limit Cycles and Center Conditions for Two Families of Kukles-Like Systems with Nilpotent Singularities

We solve theoretically the center problem and the cyclicity of the Hopf bifurcation for two families of Kukles-like systems with their origins being nilpotent and monodromic isolated singular points

Random Attractors for Stochastic Retarded Lattice Dynamical Systems

This paper is devoted to a stochastic retarded lattice dynamical system with additive white noise. We extend the method of tail estimates to stochastic retarded lattice dynamical systems and prove the existence of a compact global random attractor within the set of tempered random bounded sets

Interactions between Glucocorticoid Treatment and Cis-Regulatory Polymorphisms Contribute to Cellular Response Phenotypes

Glucocorticoids (GCs) mediate physiological responses to environmental stress and are commonly used as pharmaceuticals. GCs act primarily through the GC receptor (GR, a transcription factor). Despite their clear biomedical importance, little is known about the genetic architecture of variation in GC response. Here we provide an initial assessment of variability in the cellular response to GC treatment by profiling gene expression and protein secretion in 114 EBV-transformed B lymphocytes of African and European ancestry. We found that genetic variation affects the response of nearby genes and exhibits distinctive patterns of genotype-treatment interactions, with genotypic effects evident in either only GC-treated or only control-treated conditions. Using a novel statistical framework, we identified interactions that influence the expression of 26 genes known to play central roles in GC-related pathways (e.g. NQO1, AIRE, and SGK1) and that influence the secretion of IL6

Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales

This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper

Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise

In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. At last, we get the upper semicontinuity of random attractor

Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains

This paper is devoted to a stochastic retarded reaction-diffusion equation on all d-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. Then, we establish the existence of a random attractor for the random equation. And the existence of a random attractor for the stochastic equation follows from the conjugation relation between two random dynamical systems. The pullback asymptotic compactness is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique

Random attractors for stochastic retarded strongly damped wave equations with additive noise on bounded domains

In this paper we study the asymptotic behavior for a class of stochastic retarded strongly damped wave equation with additive noise on a bounded smooth domain in ℝd. We get the existence of the random attractor for the random dynamical systems associated with the equation