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Volume 39, Issue 3
Nonisospectral Lotka–Volterra Systems as a Candidate Model for Food Chain

Xiao-Min Chen & Xing-Biao Hu

DOI: 10.4208/aam.OA-2023-0014

Ann. Appl. Math., 39 (2023), pp. 281-322.

Published online: 2023-09

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  • Abstract

In this paper, we derive a generalized nonisospectral semi-infinite Lotka–Volterra equation, which possesses a determinant solution. We also give its a Lax pair expressed in terms of symmetric orthogonal polynomials. In addition, if the simplified case of the moment evolution relation is considered, that is, without the convolution term, we also give a generalized nonisospectral finite Lotka–Volterra equation with an explicit determinant solution. Finally, an application of the generalized nonisospectral continuous-time Lotka–Volterra equation in the food chain is investigated by numerical simulation. Our approach is mainly based on Hirota’s bilinear method and determinant techniques.

  • Keywords

Nonisospectral Lotka–Volterra, symmetric orthogonal polynomials, food chains, determinant techniques, Hirota’s bilinear method.

  • AMS Subject Headings

35Q92, 37K60, 94A11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-39-281, author = {Chen , Xiao-Min and Hu , Xing-Biao}, title = {Nonisospectral Lotka–Volterra Systems as a Candidate Model for Food Chain}, journal = {Annals of Applied Mathematics}, year = {2023}, volume = {39}, number = {3}, pages = {281--322}, abstract = {

In this paper, we derive a generalized nonisospectral semi-infinite Lotka–Volterra equation, which possesses a determinant solution. We also give its a Lax pair expressed in terms of symmetric orthogonal polynomials. In addition, if the simplified case of the moment evolution relation is considered, that is, without the convolution term, we also give a generalized nonisospectral finite Lotka–Volterra equation with an explicit determinant solution. Finally, an application of the generalized nonisospectral continuous-time Lotka–Volterra equation in the food chain is investigated by numerical simulation. Our approach is mainly based on Hirota’s bilinear method and determinant techniques.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0014}, url = {http://global-sci.org/intro/article_detail/aam/21995.html} }
TY - JOUR T1 - Nonisospectral Lotka–Volterra Systems as a Candidate Model for Food Chain AU - Chen , Xiao-Min AU - Hu , Xing-Biao JO - Annals of Applied Mathematics VL - 3 SP - 281 EP - 322 PY - 2023 DA - 2023/09 SN - 39 DO - http://doi.org/10.4208/aam.OA-2023-0014 UR - https://global-sci.org/intro/article_detail/aam/21995.html KW - Nonisospectral Lotka–Volterra, symmetric orthogonal polynomials, food chains, determinant techniques, Hirota’s bilinear method. AB -

In this paper, we derive a generalized nonisospectral semi-infinite Lotka–Volterra equation, which possesses a determinant solution. We also give its a Lax pair expressed in terms of symmetric orthogonal polynomials. In addition, if the simplified case of the moment evolution relation is considered, that is, without the convolution term, we also give a generalized nonisospectral finite Lotka–Volterra equation with an explicit determinant solution. Finally, an application of the generalized nonisospectral continuous-time Lotka–Volterra equation in the food chain is investigated by numerical simulation. Our approach is mainly based on Hirota’s bilinear method and determinant techniques.

Chen , Xiao-Min and Hu , Xing-Biao. (2023). Nonisospectral Lotka–Volterra Systems as a Candidate Model for Food Chain. Annals of Applied Mathematics. 39 (3). 281-322. doi:10.4208/aam.OA-2023-0014
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