Traveling Waves of Modified Leslie-Gower Predator-prey Systems

The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results

A sufficient condition on successful invasion by the predator

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of the prey. This proof heavily depends on comparison principle of scalar monostable equation, the rescaling method and phase-plane analysis

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined

Offset quantum-well method for tunable distributed Bragg reflector lasers and electro-absorption modulated distributed feedback lasers

A two-section offset quantum-well structure tunable laser with a tuning range of 7 nm was fabricated using offset quantum-well method. The distributed Bragg reflector (DBR) was realized just by selectively wet etching the multiquantum-well (MQW) layer above the quaternary lower waveguide. A threshold current of 32 mA and an output power of 9 mW at 100 mA were achieved. Furthermore, with this offset structure method, a distributed feedback (DFB) laser was integrated with an electro-absorption modulator (EAM), which was capable of producing 20 dB of optical extinction

Application of fuzzy random finite element method on rotor dynamics

Fuzzy and stochastic characteristics of parameters exist widely in rotating machinery. To research the parameters characteristics is of great significance in rotor dynamics. Dynamic characteristics of rotor system are analyzed taking into account uncertain properties of fuzzy and stochastic coexisting. Fuzzy variables are transformed into stochastic variables based on information entropy theory. The Neumann stochastic finite element method based on Neumann expansion combined with Newmark-β method is used in linear and nonlinear rotor system within the frame work of Monte Carlo simulation. Critical speed and dynamic response of fuzzy stochastic rotor systems are described by the proposed method. The results show that the Neumann stochastic finite element method has good applicability and efficiency in rotor dynamics