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Propagation Dynamics in a Heterogeneous Reaction-Diffusion System Under a Shifting Environment

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Abstract

We consider the propagation dynamics of a general heterogeneous reaction-diffusion system under a shifting environment. By developing the fixed-point theory for second order non-autonomous differential system and constructing appropriate upper and lower solutions, we show there exists a nondecreasing wave front with the speed consistent with the habitat shifting speed. We further show the uniqueness of forced waves by the sliding method and some analytical skills, and we obtain the global stability of forced waves by applying the dynamical systems approach. Moreover, we establish the spreading speed of the system by appealing to the abstract theory of monotone semiflows. Applications and numerical simulations are also given to illustrate the analytical results.

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Acknowledgements

We are very grateful to the anonymous referees for their careful reading and valuable suggestions which have led to an improvement of the the paper.

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Authors and Affiliations

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

    Chufen Wu

  2. Department of Mathematics, Jinan University, Guangzhou, 510632, China

    Zhaoquan Xu

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  1. Chufen Wu
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  2. Zhaoquan Xu
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Correspondence to Zhaoquan Xu.

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C. Wu was supported by the NSF of China (No. 12071074), Guangdong Basic and Applied Basic Research Foundation (No. 2019A1515011648). Z. Xu was supported by the NSF of China (No. 12071182,   No. 11701216), NSF of Guangdong Province (No. 2017A030313015) and the Fundamental Research Funds for the Central Universities.

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Wu, C., Xu, Z. Propagation Dynamics in a Heterogeneous Reaction-Diffusion System Under a Shifting Environment. J Dyn Diff Equat 35, 493–521 (2023). https://doi.org/10.1007/s10884-021-10018-0

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