Abstract
This paper proposes a single species system under seasonal succession and impulsive perturbations. The system is composed of two processes: one governed by the Gompertz equation, and the other modelled by the Logistic equation. The two processes are connected by impulse perturbations. Some very general, weak criteria on the permanence, existence, uniqueness and global stability of the positive periodic solution are established by analysis approaches based on the theory of discrete dynamical systems. The theoretical results are demonstrated by special examples and numerical simulations.
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Acknowledgements
We thank the anonymous referees very much for their valuable suggestions and careful reading and checking this paper. This work was supported by the National Natural Science Foundation of P.R. China (11361059, 11271312), the Natural Science Foundation of Xinjiang Province of China (2014721014) and the Scientific Research Programmes of Colleges in Xinjiang (XJEDU2013I03).
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Li, Y., Zhang, L. & Teng, Z. Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations. Int J Geomath 8, 241–260 (2017). https://doi.org/10.1007/s13137-017-0092-9
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DOI: https://doi.org/10.1007/s13137-017-0092-9