Abstract
In this paper, we study the quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction
under homogeneous Neumann boundary conditions in a smoothly bounded domain \(\varOmega \subset \mathbb {R}^{n}(n\ge 1)\), where \( \chi , \xi , \alpha , \beta , \gamma , \delta , \rho , a_{1},a_{2},\) \(b_{1},b_{2}\) are positive parameters, the functions \(D_{i} \in C^{2}([0,\infty ))\) and \(S_{i}\in C^{2}([0,\infty ))\) with \(S_{i}(0)=0(i=1,2)\). Firstly, under certain suitable conditions, we prove that the system admits a unique globally bounded classical solution when \(n\le 4\). Moreover, we investigate the asymptotic stability and precise convergence rates of globally bounded solutions by constructing appropriate Lyapunov functionals. Finally, we present numerical simulations that not only support our theoretical results, but also involve new and interesting phenomena.
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Acknowledgements
The authors would like to deeply thank the editor and anonymous reviewers for their insightful and constructive comments. Pan Zheng is deeply grateful to Professor Renjun Duan for his support and help at CUHK.
Funding
The work is partially supported by National Natural Science Foundation of China (Grant Nos: 11601053, 12271064), the Science and Technology Research Project of Chongqing Municipal Education Commission (Grant No: KJZD-K202200602), Natural Science Foundation of Chongqing (Grant No: CSTB2023NSCQ-MSX0099), The Hong Kong Scholars Program (Grant Nos: XJ2021042, 2021-005) and Young Hundred Talents Program of CQUPT in 2022–2024.
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Wan, C., Zheng, P. & Shan, W. On a quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction. J. Evol. Equ. 23, 78 (2023). https://doi.org/10.1007/s00028-023-00931-w
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DOI: https://doi.org/10.1007/s00028-023-00931-w