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Propagation dynamics for lattice differential equations in a time-periodic shifting habitat

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Abstract

This paper deals with the propagation dynamics for lattice differential equations in a time-periodic shifting habitat. We prove the existence, uniqueness and global exponential stability of the periodic forced waves. We also establish the spreading properties of the solutions. Our results indicate that the long-time behaviors of solutions depend on the speed of the shifting habitat and a number that is determined by the average of the maximum linearized growth rate and the diffusion coefficient.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions which have led to an improvement of the presentation.

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, People’s Republic of China

    Li-yan Pang & Shi-Liang Wu

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  1. Li-yan Pang
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Shi-Liang Wu: Partially supported by the NSF of China (No. 11671315) and Natural Science Basic Research Program of Shaanxi (No. 2020JC-24)

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Pang, Ly., Wu, SL. Propagation dynamics for lattice differential equations in a time-periodic shifting habitat. Z. Angew. Math. Phys. 72, 93 (2021). https://doi.org/10.1007/s00033-021-01522-w

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