Global dynamics of a predator-prey system with Holling type II functional response

In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSalle invariance principle, it is proven that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium

Hierarchical quantum master equation with semiclassical Drude dissipation

We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an improved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple modification but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two--level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. We also present a criterion, which depends only on the system--bath coupling strength, characteristic bath memory time, and temperature, to estimate the performance of the hierarchical quantum master equation.Comment: 10 pages, 8 figures, submitted to J. Chem. Phys. on 2009-08-0

Charge trapping and detrapping in polymeric materials: Trapping parameters

Space charge formation in polymeric materials can cause some serious concern for design engineers as the electric field may severely be distorted, leading to part of the material being overstressed. This may result in material degradation and possibly premature failure at the worst. It is therefore important to understand charge generation, trapping, and detrapping processes in the material. Trap depths and density of trapping states in materials are important as they are potentially related to microstructure of the material. Changes in these parameters may reflect the aging taken place in the material. In the present paper, characteristics of charge trapping and detrapping in low density polyethylene (LDPE) under dc electric field have been investigated using the pulsed electroacoustic (PEA) technique. A simple trapping and detrapping model based on two trapping levels has been used to qualitatively explain the observation. Numerical simulation based on the above model has been carried out to extract parameters related to trapping characteristics in the material. It has been found that the space charge decaying during the first few hundred seconds corresponding to the fast changing part of the slope was trapped with the shallow trap depth 0.88 eV, with trap density 1.47 × 1020 m-3 in the sample volume measured. At the same time, the space charge that decays at longer time corresponding to the slower part of the slope was trapped with the deep trap depth 1.01 eV, with its trap density 3.54 × 1018 m-3. The results also indicate that trap depths and density of both shallow and deep traps may be used as aging markers as changes in the material will certainly affect trapping characteristics in terms of trap depth and density

Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay

A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results

Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence

A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state

Global Stability of a Virus Infection Model with Time Delay and Absorption

In this paper, a virus infection model with time delay and absorption is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using comparison arguments, it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the basic reproduction ratio is greater than unity, sufficient conditions are derived for the global stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results

3′,6′-Bis(ethyl­amino)-2′,7′-dimethyl-2-{2-(E)-[(thio­phen-2-yl)methyl­idene­amino]­eth­yl}spiro­[isoindoline-1,9′-xanthen]-3-one methanol monosolvate

The title compound, C33H34N4O2S·CH3OH, was prepared as a spiro­lactam ring formation of rhodamine 6 G dye for comparison with a ring-opened form. The xanthene and spiro­lactam rings are approximately planar [r.m.s. deviations from planarity = 0.122 (3) and 0.072 (6) Å, respectively]. The dihedral angles formed by the spiro­lactam and thio­phene rings with the xanthene ring system are 89.7 (6) and 86.5 (2)°, respectively. The crystal structure features N—H⋯O and C—H⋯O hydrogen bonds