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Spatial Movement with Distributed Memory and Maturation Delay

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Abstract

Distributed memory reflects the phenomenon that memory can decay over time. In this paper, we are concerned with the joint effect of distributed memory and maturation delay on spatiotemporal dynamics of the model that illustrates spatial movement of animals. Without maturation delay, distributed memory with weak temporal kernel gives rise to Turing and double Turing bifurcations and there is no Hopf bifurcation. When maturation delay exists, it has been shown that the joint effect of distributed memory and maturation delay can lead to rich dynamics due to the occurrence of double Hopf, Turing–Hopf, codimension 3 and codimension 4 bifurcations. The Wright–Hutchinson equation and its modification are employed to illustrate the theoretical results and maturation delay-induced stability switches, spatially inhomogeneous steady states/periodic solutions and quasi-periodic solution are found.

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Acknowledgements

The first author is partially supported by the National Natural Science Foundation of China (No. 12201117). The second author is supported by the National Natural Science Foundation of China (No. 12371166) and the Zhejiang Provincial Natural Science Foundation of China (No. LZ23A010001).

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Authors and Affiliations

  1. School of Mathematics and Big Data, Foshan University, Foshan, 528000, China

    Shuhao Wu

  2. School of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China

    Yongli Song

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  1. Shuhao Wu
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Wu, S., Song, Y. Spatial Movement with Distributed Memory and Maturation Delay. Qual. Theory Dyn. Syst. 23, 117 (2024). https://doi.org/10.1007/s12346-024-00975-4

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