Search

A Holling-Ⅱ predator-prey diffusion model with fear effect and modification under homogeneous Dirichlet boundary conditions is studied. Firstly, the prior estimation of the model is given by applying the maximum value principle and comparison theorem. Then, by calculating the fixed point index of the cone map, the sufficient condition for the existence of the positive solution is obtained. When H is sufficiently large, the stability of the positive solution is discussed according to the linear stability theory. Finally, by means of spectral analysis and branching theorem, the existence and stability of local branching solutions are discussed with m as the branching parameter.(研究了在齐次Dirichlet边界条件下一类具有恐惧效应及修正的Holling-Ⅱ捕食者-食饵扩散模型。首先，利用极大值原理和比较定理给出模型的先验估计；然后，通过计算锥映射不动点指标，得到正解存在的充分条件，且根据线性稳定性理论，讨论了当H充分大时正解的稳定性；最后，借助谱分析和分支定理，以m为分支参数，讨论了局部分支解的存在性与稳定性。)

This paper is concerned with the existence results for generalized transition waves of space periodic and time heterogeneous lattice Fisher-KPP equations. By constructing appropriate subsolutions and supersolutions, we show that there is a critical wave speed such that a transition wave solution exists as soon as the least mean of wave speed is above this critical speed. Moreover, the critical speed we construct is proved to be minimal in some particular cases, such as space-time periodic or space independent. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the spatial spreading speeds and traveling wave solutions of cooperative systems in space-time periodic habitats with nonlocal dispersal. It is assumed that the trivial solution u = 0 of such a system is unstable and the system has a stable space-time periodic positive solution u∗(t, x). We first show that in any direction ξ ∈ SN -1, such a system has a finite spreading speed interval, and under certain condition, the spreading speed interval is a singleton set, and hence, the system has a single spreading speed c∗(ξ) in the direction of ξ. Next, we show that for any c > c∗(ξ), there are space-time periodic traveling wave solutions of the form u(t, x) = Φ(x - ctξ, t, ctξ) connecting u∗ and 0, and propagating in the direction of ξ with speed c, where Φ(x, t, y) is periodic in t and y, and there is no such solution for c < c∗(ξ). We also prove the continuity and uniqueness of space-time periodic traveling wave solutions when the reaction term is strictly sub-homogeneous. Finally, we apply the above results to nonlocal monostable equations and two-species competitive systems with nonlocal dispersal and space-time periodicity. [ABSTRACT FROM AUTHOR]