# American Institute of Mathematical Sciences

• Previous Article
Relaxation oscillations in a spruce-budworm interaction model with Holling's type II functional response
• DCDS-B Home
• This Issue
• Next Article
Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response

## Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment

 School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

* Corresponding author: Ling Zhou

Received  January 2020 Revised  July 2020 Published  August 2020

In this paper we study a nonlocal diffusion model with double free boundaries in time periodic environment, which is the natural extension of the free boundary model in [17], where local diffusion is used to describe the population dispersal. We give the existence and uniqueness of global solution and consider the properties of principle eigenvalue of time-periodic parabolic-type eigenvalue problem. With the help of attractivity of time periodic solutions, we establish a spreading-vanishing dichotomy. The sharp criteria for spreading and vanishing are also obtained.

Citation: Weiyi Zhang, Zuhan Liu, Ling Zhou. Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020256
##### References:

show all references

##### References:
 [1] Lei Yang, Lianzhang Bao. Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1083-1109. doi: 10.3934/dcdsb.2020154 [2] Rong Wang, Yihong Du. Long-time dynamics of a diffusive epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020360 [3] Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3375-3394. doi: 10.3934/dcds.2020033 [4] Maoli Chen, Xiao Wang, Yicheng Liu. Collision-free flocking for a time-delay system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1223-1241. doi: 10.3934/dcdsb.2020251 [5] Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316 [6] Nguyen Anh Tuan, Donal O'Regan, Dumitru Baleanu, Nguyen H. Tuan. On time fractional pseudo-parabolic equations with nonlocal integral conditions. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020109 [7] Zhihua Liu, Yayun Wu, Xiangming Zhang. Existence of periodic wave trains for an age-structured model with diffusion. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021009 [8] Dong-Ho Tsai, Chia-Hsing Nien. On space-time periodic solutions of the one-dimensional heat equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3997-4017. doi: 10.3934/dcds.2020037 [9] Taige Wang, Bing-Yu Zhang. Forced oscillation of viscous Burgers' equation with a time-periodic force. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1205-1221. doi: 10.3934/dcdsb.2020160 [10] Alain Damlamian, Klas Pettersson. Homogenization of oscillating boundaries. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 197-219. doi: 10.3934/dcds.2009.23.197 [11] Xueli Bai, Fang Li. Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3075-3092. doi: 10.3934/dcds.2020035 [12] Shin-Ichiro Ei, Hiroshi Ishii. The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 173-190. doi: 10.3934/dcdsb.2020329 [13] Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1579-1613. doi: 10.3934/dcdsb.2020174 [14] Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020398 [15] Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 [16] Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 [17] Raffaele Folino, Ramón G. Plaza, Marta Strani. Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020403 [18] Klemens Fellner, Jeff Morgan, Bao Quoc Tang. Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 635-651. doi: 10.3934/dcdss.2020334 [19] Chungang Shi, Wei Wang, Dafeng Chen. Weak time discretization for slow-fast stochastic reaction-diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021019 [20] Qian Liu, Shuang Liu, King-Yeung Lam. Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3683-3714. doi: 10.3934/dcds.2020050

2019 Impact Factor: 1.27