Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples

Estimates on the first two buckling eigenvalues on spherical domains

In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].Comment: This article has been submitted for publication on 2009-04-2

Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching

This paper is concerned with the boundedness, exponential stability and almost sure asymptotic stability of stochastic functional differential equations (SFDEs) with Markovian switching. The key technique used is the method of multiple Lyapunov functions. We use two auxiliary functions to dominate the corresponding different Lyapunov function in different mode while the diffusion operator in different model is controlled by other multiple auxiliary functions. Our conditions on the diffusion operator are weaker than those in the related existing works

Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller

This paper is concerned with asymptotical stabilization for a class of delay differential equations, which undergo Hopf bifurcation at equilibrium as delay increasing. Two types of controllers, continuous-time and discrete-time delay feedback controllers, are presented. Although discrete-time control problems have been discussed by several authors, to the best of our knowledge, so few controllers relate to both delay and sampling period, and the method of Hopf bifurcation has not been seen. Here, we first give a range of control parameter which ensures the asymptotical stability of equilibrium for the continuous time controlled system. And then, for the discrete-time controller we also obtain an efficient control interval provided that the sampling period is sufficiently small. Meanwhile, we try our best to estimate a well bound on sampling period and get a more complete conclusion. Finally, the theoretical results are applied to a physiological system to illustrate the effectiveness of the two controllers

Explicit approximation of the invariant measure for SDDEs with the nonlinear diffusion term

To our knowledge, the existing measure approximation theory requires the diffusion term of the stochastic delay differential equations (SDDEs) to be globally Lipschitz continuous. Our work is to develop a new explicit numerical method for SDDEs with the nonlinear diffusion term and establish the measure approximation theory. Precisely, we construct a function-valued explicit truncated Euler-Maruyama segment process (TEMSP) and prove that it admits a unique ergodic numerical invariant measure. We also prove that the numerical invariant measure converges to the underlying one of SDDE in the Fortet-Mourier distance. Finally, we give an example and numerical simulations to support our theory.Comment: 31 pages, 2 figure

The Policy Transfer Situation among Chinese National Independent Innovation Demonstration Zones

Chinese national independent innovation demonstration zones are a major organizational mode of Chinese scientific and technological innovation, and a paragon of first movers of technological policies. Since foundation of these demonstration zones, transfer and mutual learning of policies among them have accompanied their growth. Currently, in demonstration zones, policy transfer has become a common phenomenon or even a major source of policy formation. However, due to lack of a systematic knowledge, policy transfer is still largely blind and random, thus seriously restricting the policy innovation ability of demonstration zones and making research into the policy transfer of demonstration zones imperative. This paper adopts the technological policies issued by some national independent innovation demonstration zones from 2006 to 2015 as samples. Through a comprehensive review, these policies are classified into five types, namely technological talents, technological industries, technological enterprises, technological finance and others. Based on the transfer-in and transfer-out of different policies, the development trend of policy transfer in demonstration zones is studied. Meanwhile, combining the importance degree of policy transfer-out, the competitiveness of different types of policies in demonstration zones is analyzed, and characteristics of policy transfer among Chinese demonstration zones are examined. It is hoped that this research can fill the gap of empirical research into transfer of technological policies in China. Keywords: Independent innovation, Demonstration zone, Policy transfer, Policy competitivenes