patch model
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Author(s):  
Wenhao Jia ◽  
Tao Ding ◽  
Jiawen Bai ◽  
Linquan Bai ◽  
Yongheng Yang ◽  
...  

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 817-842
Author(s):  
Shanshan Chen ◽  
Junping Shi ◽  
Zhisheng Shuai ◽  
Yixiang Wu

Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.


Author(s):  
K. Sunil Behal ◽  
Sunita Gakkhar ◽  
Tanuja Srivastava
Keyword(s):  

Trees ◽  
2021 ◽  
Author(s):  
Marta Pardos ◽  
Guillermo Madrigal ◽  
Javier de Dios-García ◽  
Javier Gordo ◽  
Rafael Calama

2021 ◽  
Vol 304-305 ◽  
pp. 108433
Author(s):  
Samuel Ortega-Farias ◽  
Wladimir Esteban-Condori ◽  
Camilo Riveros-Burgos ◽  
Fernando Fuentes-Peñailillo ◽  
Matthew Bardeen

2021 ◽  
Vol 7 (1) ◽  
pp. 536-551
Author(s):  
Lijuan Chen ◽  
◽  
Tingting Liu ◽  
Fengde Chen

<abstract><p>A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.</p></abstract>


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