Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects

Kejun Zhuang; Wenqian You; Gao Jia

doi:10.11948/20190094

2020 Volume 10 Issue 2

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Kejun Zhuang, Wenqian You, Gao Jia. Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 686-712. doi: 10.11948/20190094

Citation:

Kejun Zhuang, Wenqian You, Gao Jia. Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 686-712. doi: 10.11948/20190094

Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects

1.
School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
2.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Corresponding author: Email address:zhkj123@163.com(K. Zhuang)
Fund Project: The authors were supported by the MOE (Ministry of Education in China) Project of Humanities and Social Sciences (17YJC630175) and Anhui Provincial Quality Engineering Project (2019sxzx10)

Abstract

Abstract

In this paper, we propose a three-species reaction-diffusion planktonic system with prey-taxis and toxic effects, in which the zooplankton can recognize the nontoxic and toxin-producing phytoplankton and can make proper response. We first establish the existence and stability of the unique positive constant equilibrium solution by utilizing the linear stability theory for partial differential equations. Then we obtain the existence and properties of nonconstant positive solutions by detailed steady state bifurcation analysis. In addition, we obtain that change of taxis rate will result in the appearance of time-periodic solutions. Finally, we conduct some numerical simulations and give the conclusions.
- Planktonic system /
- reaction diffusion /
- prey-taxis /
- linear stability /
- steady state bifurcation /
- Hopf bifurcation
MSC: 35B32, 35B10, 92D40

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References

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