Periodic oscillation and tri-stability in mutualism systems with two consumers
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Abstract
This paper considers mutualistic interactions between two consumers, in which one consumer can consume a resource only by exchange of service for service with the other. By rigorous analysis on the one-resource and two-consumer model with Holling-type I response, we show periodic oscillations and tri-stability in the mutualism system: when their initial densities decrease, the consumers' interaction outcomes would change from coexistence in periodic oscillation, to persistence at a steady state, and to extinction. Under certain conditions, we also show two types of bi-stability in the system: the consumers would change from coexisting in periodic oscillation (resp. at a steady state) to going to extinction when their initial densities decrease. Then we analyze a modified system with Holling-type II response. Based on theoretical analysis and numerical computation, we show that there also exist tri-stability and two types of bi-stability in this system. Moreover, it is shown that varying the degree of obligation can lead to transition of interaction outcomes between coexistence in periodic oscillation (resp. at a steady state) and extinction of both consumers. These results are important in understanding complexity in mutualism.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Periodic oscillation and tri-stability in mutualism systems with two consumers |
| Series title | Journal of Mathematical Analysis and Applications |
| DOI | 10.1016/j.jmaa.2021.125672 |
| Volume | 506 |
| Issue | 2 |
| Year Published | 2021 |
| Language | English |
| Publisher | Elsevier |
| Contributing office(s) | Wetland and Aquatic Research Center |
| Description | 125672 |
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