Abstract
In this paper, we study a predator–prey reaction–diffusion model with seasonality and fear effect. In this model, the predator species reproduces only at a certain time of each year. We calculate the steady states of the system and study their stabilities, and then, we derive the conditions for Turing instability to occur. Numerical simulations show that (i) spatial patterns can emerge for Beddington–DeAngelis functional response, (ii) the system can have oscillatory behavior for both linear functional response and Beddington–DeAngelis functional response.
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Acknowledgements
The authors would like to thank Dr. Xiaoying Wang for sharing the numerical simulation data of paper (Wang and Lutscher 2019), which helped a lot in improving our numerical simulation codes. We thank the editors and the anonymous reviewers for their valuable comments, which helped to improve the presentation of this paper.
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This research was supported by the National Natural Science Foundation of China (No. 12071491).
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TL contributed to writing—original draft. QW contributed to writing—review and editing.
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Li, T., Wang, Q. Turing Patterns in a Predator–Prey Reaction–Diffusion Model with Seasonality and Fear Effect. J Nonlinear Sci 33, 86 (2023). https://doi.org/10.1007/s00332-023-09938-6
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DOI: https://doi.org/10.1007/s00332-023-09938-6
Keywords
- A predator–prey reaction–diffusion model
- Impulsive reproduction and fear effect
- Turing patterns
- Discrete systems