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Stoichiometric food chain model on discrete time scale

1 School of Science, Dalian Maritime University, 1 Linghai Road, Dalian, Liaoning, 116026, P. R. China
2 Center for Mathematical Biosciences, School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R. China
3 College of Science, Dalian Minzu University, 18 Liaohe West Road, Dalian, Liaoning, 116600, P R. China
4 Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409, United States
5 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Special Issues: Resource Explicit Population Models

Stoichiometry-based models can yield many new insights into producer - grazer systems. Many interesting results can be obtained from models continuous in time. There raises the question of how robust the model predictions are to time discretization. A discrete stoichiometric food-chain model is analyzed and compared with a corresponding continuous model. Theoretical and numerical results show that the discrete and continuous models have many properties in common but differences also exist. Stoichiometric impacts of producer nutritional quality also persist in the discrete system. Both types of models can exhibit qualitatively different behaviors with the same parameter sets. Discretization enlarges the parameter ranges for the existence of chaotic dynamics. Our results suggest that the stoichiometric mechanisms are robust to time discretization and the nutritional quality of the producer can have dramatic and counterintuitive impacts on population dynamics, which agrees with the existing analysis of pelagic systems.
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Keywords stoichiometry; predator-prey system; food quality; C:P ratio; discrete model

Citation: Ming Chen, Meng Fan, Congbo Xie, Angela Peace, Hao Wang. Stoichiometric food chain model on discrete time scale. Mathematical Biosciences and Engineering, 2019, 16(1): 101-118. doi: 10.3934/mbe.2019005

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