一类带时滞的阶段结构捕食模型的定性分析

研究了一类具有时滞和阶段结构的捕食模型系统,给出了系统持续生存的充分条件.利用比较定理和构造适当的Lyapunov泛函得到了该系统正平衡态全局渐近稳定的充分条件.     

Persistence of fungitoxicity of two triorganotin(IV) compounds in soil

The persistence of triphenyltin chloride-triphenylphosphine oxide (Ph₃SnCl·Ph₃PO) and diphenylbutyltin bromide (Ph₂BuSnBr) in unsterilized sandy loam soil maintained in the dark at 60% of its water-holding capacity and at 27±2°C was studied over a period of 29 days. The percentage recovery of the compounds upon extraction with acetone immediately after application to soil was 60% for Ph₃SnCl·Ph₃PO and 9.8% for Ph₂BuSnBr. The half-lives of the compounds were 15 days for Ph₃SnCl·Ph₃PO and 14.2 days for Ph₂BuSnBr. After 29 days following application of the compounds in soil < 8.3 μg g^?1 of Ph₃SnCl·Ph₃PO and < 5.1 μg g^?1 of Ph₂BuSnBr remained in soil compared with the starting concentration of 50 μg of each compound per gram soil. The two triorganotin compounds were evidently easily degraded and the compounds may be applied every 2–3 weeks in the field at a rate of at least 0.005–0.01 kg ha^?1.     

带时滞的比率型的食物链系统的持久性和稳定性

A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.     

Impact on the predator population while lethal disease spreads in the prey

An eco‐epidemiological model is proposed to interpret the impact of an infectious disease on ecosystem, where prey is infected by lethal bacteria and the consumption of infected prey contributes to the negative growth of predator population. Of course, the required time delay is incorporated into the model. The biodiversity conservation is concerned. Stability, persistence, and bifurcation are carried out. Finally, numerical simulations are performed to support the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Instability and violence in Imperial Rome: A “laboratory” for studying social contagion?

Imperial Rome with its >50% assassination rate of emperors, many of whom are depicted in history as ‘deranged’, initially appears a chaotic period of history beyond the purview of science. But time series analysis indicates this violence occurred non‐randomly: reign length was autocorrelated and demonstrated ‘memory persistence,’ and short reigns occurred in clusters. Additionally, deviations from average reign‐length occurred in patterns matching the Empire's rise and decline. A model is proposed for how army‐backed usurpation and post‐coup instability likely generated the observed cycles. The five‐century span of Imperial Rome likely makes it the longest‐lived regime with fair documentation, and potentially provides a ‘laboratory’ with ongoing relevance for studying transmission of violence and instability. © 2016 Wiley Periodicals, Inc. Complexity 21: 613–622, 2016     

PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

A three-species ratio-dependent predator-prey diffusion model with time de-lays is investigated. It is shown that the system is uniformly persistent under some ap-propriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.     

Qualitative analysis of hepatitis B virus infection model with impulsive vaccination and time delay

According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus (HBV) infection with impulsive vaccination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.     

Modeling and stability analysis for a cholera model with vaccination

In this paper, we consider a cholera model with vaccination. The disease‐free equilibrium of the system is globally asymptotically stable when the basic reproduction number . If , the disease persists and the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region under some conditions, which is obtained by compound matrices and geometric approaches. We perform sensitivity analysis of on the parameters in order to determine their relative importance to disease transmission and prevalence. Numerical simulations are presented to illustrate the results. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling and Analysis of the Epidemic Model under Pulse Charging in Wireless Rechargeable Sensor Networks

With the development of wireless sensor networks (WSNs), energy constraints and network security have become the main problems. This paper discusses the dynamic of the Susceptible, Infected, Low-energy, Susceptible model under pulse charging (SILS-P) in wireless rechargeable sensor networks. After the construction of the model, the local stability and global stability of the malware-free T-period solution of the model are analyzed, and the threshold R0 is obtained. Then, using the comparison theorem and Floquet theorem, we obtain the relationship between R0 and the stability. In order to make the conclusion more intuitive, we use simulation to reveal the impact of parameters on R0. In addition, the paper discusses the continuous charging model, and reveals its dynamic by simulation. Finally, the paper compares three charging strategies: pulse charging, continuous charging and non-charging and obtains the relationship between their threshold values and system parameters.     

Stochastic persistence and stability analysis of a modified Holling–Tanner model

The article aims to study the basic dynamical features of a modified Holling–Tanner prey–predator model with ratio‐dependent functional response. We have proved the global existence of the solution for the deterministic model. The parametric restriction for persistence of both species is also obtained along with the proof of local asymptotic stability of the interior equilibrium point(s). Conditions for local bifurcations of interior equilibrium points are provided. The global dynamic behavior is examined thoroughly with supportive numerical simulation results. Next, we have formulated the stochastic model by perturbing the intrinsic growth rates of prey and predator populations with white noise terms. The existence uniqueness of solutions for stochastic model is established. Further, we have derived the parametric restrictions required for the persistence of the stochastic model. Finally, we have discussed the stochastic stability results in terms of the first and second order moments. Numerical simulation results are provided to support the analytical findings. Copyright © 2012 John Wiley & Sons, Ltd.