MODELING THE ROLE OF CONSTANT AND TIME VARYING RECYCLING DELAY ON AN ECOLOGICAL FOOD CHAIN

Banibrata Mukhopadhyay; rnRakhi Bhattacharyya

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MODELING THE ROLE OF CONSTANT AND TIME VARYING RECYCLING DELAY ON AN ECOLOGICAL FOOD CHAIN

机译：对生态食物链上恒定和时变回收延迟的作用进行建模

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We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.

机译：我们考虑了营养-自养-草食动物与自养和草食动物的营养循环之间相互作用的数学模型。根据系统参数研究了模型的局部和全局稳定性标准。接下来，我们将从食草动物中回收营养物所需的时间作为恒定的离散时间延迟。分析所得的DDE模型的稳定性和分叉方面。最后，我们以振荡形式假设回收延迟，以模拟养分回收的每日变化并推导出可变延迟模型的稳定性标准。将可变时滞模型与恒定时延模型进行了比较，以揭示某些实际生态环境中振荡时延的生物学相关性。进行数值模拟以支持分析结果。

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来源
《Applications of Mathematics》 |2010年第3期|P.221-240|共20页
作者
Banibrata Mukhopadhyay; rnRakhi Bhattacharyya;
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作者单位

Department of Science, Central Calcutta Polytechnic, 21, Convent Road, Kolkata-700 014, India;

rnDepartment of Science, The Calcutta Technical School, 110, S. N. Baner-jee Road, Kolkata-700 013, India;

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正文语种 eng
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autotroph; herbivore; nutrient recycling; global stability; hopf-bifurcation; variable delay; two-timing expansion;

机译：自养草食动物营养循环利用;全球稳定;Hopf分支可变延迟二次定时扩展;

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1. Modeling the role of constant and time varying recycling delay on an ecological food chain [J] . Bhattacharyya Rakhi, Mukhopadhyay Banibrata Applications of mathematics . 2010,第3期

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2. ROLE OF DIFFERENT SYSTEM DELAYS ON ECOLOGICAL FOOD CHAIN DYNAMICS： MATHEMATICAL MODELLING AND ANALYSIS [J] . R. BHATTACHARYYA, Ashoke BERA, B. MUKHOPADHYAY 系统科学与复杂性：英文版 . 2010,第004期

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3. ROLE OF DIFFERENT SYSTEM DELAYS ON ECOLOGICAL FOOD CHAIN DYNAMICS: MATHEMATICAL MODELLING AND ANALYSIS [J] . R. BHATTACHARYYA, Ashoke BERA, B. MUKHOPADHYAY 系统科学与复杂性：英文版 . 2010,第004期

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7. Modeling the role of constant and time varying recycling delay on an ecological food chain [O] . Mukhopadhyay, Banibrata, Bhattacharyya, Rakhi 2010

机译：模拟恒定和时变的回收延迟在生态食物链中的作用

MODELING THE ROLE OF CONSTANT AND TIME VARYING RECYCLING DELAY ON AN ECOLOGICAL FOOD CHAIN

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