Dynamic Behaviors of Filippov Ecosystems Induced by Allee Effects

QIN Wenjie; GUAN Haiyan; WANG Peipei; TANG Guangyao

doi:10.21656/1000-0887.400169

Volume 41 Issue 4

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QIN Wenjie, GUAN Haiyan, WANG Peipei, TANG Guangyao. Dynamic Behaviors of Filippov Ecosystems Induced by Allee Effects[J]. Applied Mathematics and Mechanics, 2020, 41(4): 438-447. doi: 10.21656/1000-0887.400169

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Dynamic Behaviors of Filippov Ecosystems Induced by Allee Effects

doi: 10.21656/1000-0887.400169

¹Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P.R.China;²Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, P.R.China

Funds: The National Natural Science Foundation of China(11601268; 11761031; 11801311)

Received Date: 2019-05-10
Rev Recd Date: 2019-07-12
Publish Date: 2020-04-01

Abstract

Abstract

A non-smooth Filippov predatorprey system induced by Allee effects was proposed. The sliding domain, the sliding mode dynamics and the existence of several equilibria were discussed by means of the qualitative theory and method related to the Filippov system. Furthermore, the sliding mode bifurcation, the boundary focus bifurcation and the global dynamic behaviors were given through numerical simulations. The results indicate that, the intensity of Allee effects could make the dynamics of population become unstable, and may be unfavorable for the protection of endangered species.
- Allee effect,
- Filippov system,
- sliding mode,
- sliding bifurcation

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References(17)

References

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