title: On heteroclinic cycles of competitive maps via carrying simplices.
abstract: We concentrate on the effects of heteroclinic cycles and the interplay of heteroclinic attractors or repellers on the boundary of the carrying simplices for low-dimensional discrete-time competitive systems. Based on the existence of the carrying simplex for the competitive mapping, we provide the criteria on stability of the heteroclinic cycle. This result can be seen as a discrete counterpart of that for the continuous-time systems. Several concrete discrete-time competition models are further analyzed, which do admit heteroclinic cycles. The criteria on the stability of the heteroclinic cycle for each model are also given, which are comparable with the corresponding continuous-time models.
authors.affiliation: Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, People's Republic of China.
authors.forename: Jifa
authors.initials: J
authors.lastname: Jiang
authors.affiliation: Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, People's Republic of China. 2012_niulei@tongji.edu.cn.
authors.forename: Lei
authors.initials: L
authors.lastname: Niu
authors.affiliation: Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Wang
mesh_terms: D017753:Ecosystem; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D013045:Species Specificity
keywords: Attractor; Carrying simplex; Competitive map; Fixed point; Heteroclinic cycle; Repeller; Stability