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Delay-induced Hopf and double Hopf-bifurcation in plankton system with dormancy of predators

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Abstract

In this article, we propose a model for plankton dynamics in presence of dormancy and time delay. Dormancy is a better adaptive strategy to survive in a harsh environmental condition than active ones. The dormancy in zooplankton receives considerable interest as it reduces the environmental stress and helps to regulate the predator’s life cycle. The density of phytoplankton is affected by gestation delay and the density of zooplankton is benefited by the adaptation of dormant phase (such as resting eggs). The interaction between the phytoplankton and zooplankton is taken as Beddington–DeAngelis (B-D)-type functional response. The feasibility and boundedness criterion of the considered model system are proved by the comparison principle. We have discussed the stability and direction of bifurcating periodic solution by applying the normal form theory and center manifold arguments. Computational illustrations are executed to support analytical findings by plotting the bifurcation diagram, time evolution plot and phase portraits for biologically feasible parameter values. Our numerical results revealed that the system depicts chaotic attractor as the magnitude of feedback time delay beyond the threshold value but the system behavior may become stable for some parametric values.

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Acknowledgements

This research work is supported by Science and Engineering Research Board (SERB), Govt. of India under the Grant No. EMR/2017/000607 to the corresponding author (Nilesh Kumar Thakur).

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  1. Department of Mathematics, National Institute of Technology Raipur, Raipur, CG, 492010, India

    Archana Ojha & Nilesh Kumar Thakur

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  1. Archana Ojha
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Correspondence to Nilesh Kumar Thakur.

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Ojha, A., Thakur, N.K. Delay-induced Hopf and double Hopf-bifurcation in plankton system with dormancy of predators. Nonlinear Dyn 105, 997–1018 (2021). https://doi.org/10.1007/s11071-021-06617-7

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