Stability analysis of a system of second‐order difference equations

In this paper, we study the boundedness character and persistence, existence and uniqueness of the positive equilibrium, local and global behavior, and the rate of convergence of positive solutions of the following system of rational difference equations where the parameters α_i,β_i,a_i,b_i for i∈{1,2} and the initial conditions x_?1,x₀,y_?1,y₀ are positive real numbers. Some numerical example are given to verify our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

In this paper, we propose a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects and investigate its stochastic dynamics. We first prove that the subsystem of the system has a unique periodic solution which is globally attractive. Furthermore, we obtain the threshold value in the mean which governs the stochastic persistence and the extinction of the prey–predator system. Our results show that the stochastic noises and impulsive perturbations have crucial effects on the persistence and extinction of each species. Finally, we use the different stochastic noises and impulsive effects parameters to provide a series of numerical simulations to illustrate the analytical results.     

Scaling Laws of Bottle‐Brush Polymers in Dilute Solutions

The structural determination and manipulation of bottle‐brush polymers, a class of polymers with serially grafted side‐chains, is challenging due to the interplay of side‐chain and backbone interactions over various length scales. The present work performs a detailed analysis, using molecular dynamics simulation techniques, to unravel these interactions by probing the distinct rod to a flexible real‐chain with self‐avoiding walk (SAW) type crossover in the backbone static structure factor. This analysis elucidates the deviation from flexible chain behavior, while also providing a quantitative measure of persistence length, . Significantly, the results identify a trend in which is consistent with the debated theoretical prediction of , where N_s is the number of monomers in each side‐chain of the bottle‐brush polymer.

     

Global dynamics of a competitive system of rational difference equations

In this paper, we study the qualitative behavior of a competitive system of second‐order rational difference equations. More precisely, we investigate the boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the system. Some numerical examples are given to verify our theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

A STAGE-STRUCTURED AND HARVESTING PREDATOR-PREY SYSTEM

A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out t...     

具毒素影响的二维Kolmogorov模型的生存分析

对具毒素影响的二维Kolmogorov模型进行研究,利用积分均值法,得到了各种群平均持续生存和绝灭的阈值,并得到了外界输入率的阈值.     

具有时滞和脉冲输入的一类双资源和两种微生物恒化器模型的分析

考虑一类双资源和两种微生物且具有时滞和脉冲输入的恒化器模型,证明了微生物灭绝周期解的存在性,并得到该周期解全局吸引性的临界条件和系统持久的充分条件,最后利用数值模拟结果说明本文的主要结论.     

Dynamics of poly(p‐phenylene) ladder polymers in solution

Photon correlation spectroscopy in both polarized and depolarized geometry was employed to investigate the dynamics of a ribbon‐type polymer exhibiting good solubility. In dilute solution, the translational diffusion for all examined molecular weights has confirmed the picture of wormlike chains with rather short (∼ 7 nm) persistence length (Macromolecules 1997, 30, 273). In the semidilute regime, the total concentration fluctuations display, besides the fast dominant cooperative diffusion, a second slower diffusive process that exhibits weak concentration dependence and is not related to the self‐diffusion measured by pulse‐field‐gradient NMR. The concentration dependence of the cooperative and the self‐diffusion coefficient as well as of the zero‐shear viscosity cannot be consistently described by neither flexible nor stiff chain models. Presence of aggregates was revealed at high concentrations. Owing to the short persistence length, the rotational diffusion is too fast to be adequately investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2211–2220, 1999     

Chain conformation of rod-like polymers in the melt: Small-angle neutron scattering of poly(benzoyl paraphenylene)

The chain conformation of a rigid rod polymer, poly(benzoyl paraphenylene), is determined in the melt using small-angle neutron scattering. The coherent scattering cross-section from blends of partially deuterated and hydrogenous poly(benzoyl paraphenylene) agree well with ideal rod scattering for q > 0.02 Å⁻¹, indicating that the polymer chains are highly extended. Comparison of the results to a single chain-scattering function for chains of arbitrary stiffness yield a persistence length of ca. 130 Å. Pure component scattering at the lowest scattering lengths indicate that the melt is not molecularly homogenous, but is comprised of domains, potentially reflecting localized groupings of chains with similar backbone orientation. Furthermore, this mesoscopic structure depends on the processing history of the polymer in the melt state. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2449–2459, 1998     

Persistence in a three species Lotka-Volterra nonperiodic predator-prey system

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