Study in two new patchy ecosystem models with commensalism

Abstract In this paper, two new patchy ecosystem models with commensalism are proposed. The environmental capacity of one species is enhanced due to commensalism. When the species has logical growth, commensalism can only increase the density. However, when the species has strong Allee effect, commensalism has great influence on the dynamic behavior of the system such as the emergence of the positive equilibrium and saddle-node bifurcation. Also, once the strong Allee effect is incorporated, the corresponding model has bistable attractors including a stable boundary equilibrium and a stable positive equilibrium. Commensalism is beneficial to the persistence of the species. 2000 Mathematics Subject Classification 34C25; 92D25; 34D20; 34D40