Convergence and stability for essentially strongly order-preserving semiflows

This paper is concerned with a class of essentially strongly order-preserving semiflows, which are defined on an ordered metric space and are generalizations of strongly order-preserving semiflows. For essentially strongly order-preserving semiflows, we prove several principles, which are analogues of the nonordering principle for limit sets, the limit set dichtomy and the sequential limit set trichotomy for strongly order-preserving semiflows. Then, under certain compactness hypotheses, we obtain some results on convergence, quasiconvergence and stability in essentially strongly order-preserving semiflows. Finally, some applications are made to quasimonotone systems of delay differential equations and reaction-diffusion equations with delay, and the main advantages of our results over the classical ones are that we do not require the delicate choice of state space and the technical ignition assumption.     

New generic quasi-convergence principles with applications

In this paper, essentially strongly order-preserving and conditionally set-condensing semiflows are considered. Obtained is a new type of generic quasi-convergence principles implying the existence of an open and dense set of stable quasi-convergent points when the state space is order bounded. The generic quasi-convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations, giving some results of theoretical and practical significance.     

Convergence of a class of discrete-time semiflows with applications to difference systems

In this paper, by employing comparison technique and invariance properties of a positively limited set, we investigate the convergence of precompact orbits of a class of discrete-time semiflows. In particular, we consider the convergence of precompact orbits of discrete-time semiflows generated by some monotone mapping. We then apply these abstract results to a class of difference systems to obtain the large-time behavior of solutions. Our results improve and extend some existing ones.     

Convergence for pseudo monotone semiflows on product ordered topological spaces

In this paper, we consider a class of pseudo monotone semiflows, which only enjoy some weak monotonicity properties and are defined on product-ordered topological spaces. Under certain conditions, several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium, which improve and extend some corresponding results already known. Some applications to delay differential equations are presented.     

Convergence of a class of discrete-time semiflows with application to neutral delay differential equations

In this paper, we introduce a class of pseudo-monotone maps on ordered topological spaces. By exploiting monotonicity methods and the invariance of the omega limit set, we establish a convergence principle for discrete-time semiflows generated by the maps introduced. The convergence principle is then applied to a class of periodic neutral delay differential equations, which leads to some novel and sharper results.     

Persistence and propagation of a discrete-time map and PDE hybrid model with strong Allee effect

Persistence and propagation of species are fundamental questions in spatial ecology. This paper focuses on the impact of Allee effect on the persistence and propagation of a population with birth pulse. We investigate the threshold dynamics of an impulsive reaction–diffusion model and provide the existence of bistable traveling waves connecting two stable equilibria. To prove the existence of bistable waves, we extend the method of monotone semiflows to impulsive reaction–diffusion systems. We use the methods of upper and lower solutions and the convergence theorem for monotone semiflows to prove the global stability of traveling waves and their uniqueness up to translation. Then we enhance the stability of bistable traveling waves to global exponential stability. Numerical simulations illustrate our theoretical results.     

混合单调半流与泛函微分方程的稳定性

本文首先提出混合单调半流的概念和泛函微分方程生成这种半流的条件。然后，利用半流的混合单调性，我们得到关于泛函微分方程的渐近稳定性和全局稳定性的新结果．     

On Quadratic g-Evaluations/Expectations and Related Analysis

This work is concerned with coupling and exponential convergence rate for a class of Markovian switching jump-diffusion processes. The processes under consideration can be thought of as a number of jump-diffusion processes modulated by a Markovian switching device. For this class of processes, we construct some order-preserving couplings. Furthermore, by virtue of the coupling results, we also provide an estimate of exponential convergence rate for the Markovian switching jump-diffusion processes without Gaussian noise.     

一类单调斜积半流的ω-极限集的提升动力学行为

本文研究了一类具有极小基流的单调斜积半流.在假定半流存在-个半连续的半平衡的前提下,我们证明了具有某种一致稳定性的正半轨线的ω极限集具有1-covering性质,这为理解系统的全局动力学提供了几何洞察.     

关于Ishikawa迭代程序稳定性的注释

在实一致光滑Banach空间中，研究了一类具有值域有界、连续强伪压缩算子和连续强增生算子的Ishikawa迭代程序的稳定性；给出了迭代程序中参数所满足的条件，并证明了迭代过程的收敛性。所得结果改进和扩展近期相关结果，为进一步讨论带误差迭代程序的收敛性提供理论依据。