Affiliation:
1. College of Mathematics and Statistics Fuzhou University No. 2, wulongjiang Avenue, Minhou County, Fuzhou CHINA
Abstract
A Lotka-Volterra commensal symbiosis model with a density dependent birth rate and a Merdan-type Allee effect on the second species has been proposed and examined. The global attractivity of system’s equilibria is ensured by using the differential inequality theory. Our results show that the Allee effect has no effect on the existence or stability of the system’s equilibrium point. However, both species take longer to approach extinction or a stable equilibrium state as the Allee effect increases.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Subject
General Agricultural and Biological Sciences,General Biochemistry, Genetics and Molecular Biology,General Medicine,General Neuroscience
Reference27 articles.
1. R. X. Wu, L. Li, X. Y. Zhou, A commensal symbiosis model with Holling type functional response, Journal of Mathematics and Computer Science, 16 (2016), 364-371.
2. J. H. Chen, R. X. Wu, A commensal symbiosis model with non-monotonic functional response, Commun. Math. Biol. Neurosci. Vol 2017 (2017), Article ID 5.
3. R. X. Wu, L. Li, Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently, Journal of Mathematics and Computer Science, 16 (2016) 495-506.
4. R. X. Wu, L. Lin, Q. F. Lin, A Holling type commensal symbiosis model involving Allee effect, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 5.
5. T. T. Li, Q. X. Lin, J. H. Chen, Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response, Communications in Mathematical Biology and Neuroscience, Vol 2016 (2016), Article ID 22.