Stoichiometric food chain model on discrete time scale

Mathematical Biosciences and Engineering

Ming Chen¹  Meng Fan²  Congbo Xie³  Angela Peace⁴  Hao Wang⁵ 

[1] 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;

关键词: stoichiometry;    predator-prey system;    food quality;    c:p ratio;    discrete model;   

DOI  :  10.3934/mbe.2019005

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown