Analysis of the Dynamics of a Predator-prey Model with Holling Functional Response

A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling \uppercase\expandafter{\romannumeral2} functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.     

Time-Delay Characteristics of Complex Lü System and Its Application in Speech Communication

Although complex Lü systems have been considered in many studies, application of the self-time-delay synchronization (STDS) of complex Lü systems in secure speech communications does not appear to have been covered in much of the literature. Therefore, it is meaningful to study the STDS of complex Lü systems and its application in secure speech communication. First, a complex Lü system with double time-delay is introduced and its chaotic characteristics are analyzed. Second, a synchronization controller is designed to achieve STDS. Third, the improved STDS controller is used to design a speech communication scheme based on a complex Lü system. Finally, the effectiveness of the controller and communication scheme are verified by simulation.     

一维双极量子能量输运稳态模型弱解的存在性

在一维有界区域上研究一个半导体双极量子能量输运稳态模型.将此模型变形为由2个四阶椭圆方程和1个二阶退化椭圆方程组成的耦合方程组.利用截断方法和Leray-Schauder不动点定理证明了其变形后方程组弱解的存在性.     

Investigating the Turing Conditions for Diffusion-driven Instability in Predator-prey System with Hunting Cooperation Functional Response

In this paper, we focus on stability analysis of steady-state solutions of a predator-prey system with hunting cooperation functional response. The results show that the Turing instability can be affected not only the existence of hunting cooperation, but also the diffusion coefficients: (1) in the absence of predator diffusion, diffusion-driven instability can be induced by hunting cooperation, but no stable patterns appear; (2) the system can occur diffusion-driven instability and Turing patterns, when both predator and prey have diffusion, and the diffusion coefficient of prey is greater than that of the predator. The numerical simulations of two cases are presented to verify the validity of our theoretical results.     

The effect of prey refuge and time delay on a diffusive predator‐prey system with hyperbolic mortality

In this article, we investigate the effect of prey refuge and time delay on a diffusive predator‐prey system with Holling II functional response and hyperbolic mortality subject to Neumann boundary condition. More precisely, we study Turing instability of positive equilibrium by using refuge as parameter, instability and Hopf bifurcation induced by time delay. In addition, by the theory of normal form and center manifold, we derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. © 2016 Wiley Periodicals, Inc. Complexity 21: 446–459, 2016     

Codimension-two bifurcation analysis of the continuous stirred tank reactor model with delay

The aim of this paper is to research the dynamical behaviors of the continuous stirred tank reactor (CSTR) model with delay. Firstly, we discuss the situation that its related characteristic equation has a simple zero root and a pair of purely imaginary roots. Secondly, the center manifold method and the normal form method are used to reduce the equation of CSTR model. Finally, some characteristics about the CSTR model can be obtained. We analyze three different topological structure and give entire bifurcation diagrams and phase portraits, which are innovative phenomenon. At the end, we obtain the stable and unstable periodic solutions by numerical simulation.     

Metal-catalyzed rearrangement of cyclopropenes to allenes

A novel transition-metal-catalyzed rearrangement of silylated cyclopropenes to the corresponding allenes is described. The presence of both the trimethylsilyl group on the cyclopropene and the platinum catalyst are crucial for this rearrangement.     

Synthesis of 3-substituted indazoles from arynes and N-tosylhydrazones

Readily available, stable, and inexpensive N-tosylhydrazones react with arynes under mild reaction conditions to afford 3-substituted indazoles in moderate to good yields. The reaction appears to involve a dipolar cycloaddition of in situ generated diazo compounds and arynes.     

Highly enantioselective deracemization of linear and vaulted biaryl ligands

[reaction: see text] A copper-mediated deracemization of the vaulted biaryl ligands VANOL and VAPOL can be readily achieved in the presence of (-)-spartiene. The optimal procedure involves the in situ generation of copper(II) and leads to the reproducible formation of (S)-VANOL and (S)-VAPOL in greater than 99% ee from the racemates. This method is superior to existing procedures for BINOL (92% ee).