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Volume 5, Issue 3
Dynamics of a Discrete Two-Species Competitive Model with Michaelies-Menten Type Harvesting in the First Species

Xin Jin & Xianyi Li

DOI: 10.12150/jnma.2023.494

J. Nonl. Mod. Anal., 5 (2023), pp. 494-523.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results.

  • Keywords

Competitive model with Michaelis-Menten type harvesting, semidiscretization method, transcritical bifurcation, period-doubling bifurcation, pitchfork bifurcation.

  • AMS Subject Headings

39A28, 39A30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-494, author = {Jin , Xin and Li , Xianyi}, title = {Dynamics of a Discrete Two-Species Competitive Model with Michaelies-Menten Type Harvesting in the First Species}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {494--523}, abstract = {

In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.494}, url = {http://global-sci.org/intro/article_detail/jnma/21948.html} }
TY - JOUR T1 - Dynamics of a Discrete Two-Species Competitive Model with Michaelies-Menten Type Harvesting in the First Species AU - Jin , Xin AU - Li , Xianyi JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 494 EP - 523 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.494 UR - https://global-sci.org/intro/article_detail/jnma/21948.html KW - Competitive model with Michaelis-Menten type harvesting, semidiscretization method, transcritical bifurcation, period-doubling bifurcation, pitchfork bifurcation. AB -

In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results.

Xin Jin & Xianyi Li. (2023). Dynamics of a Discrete Two-Species Competitive Model with Michaelies-Menten Type Harvesting in the First Species. Journal of Nonlinear Modeling and Analysis. 5 (3). 494-523. doi:10.12150/jnma.2023.494
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