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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.

Jin , Xin and Li , Xianyi. (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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