IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n745296.html
   My bibliography  Save this article

Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays

Author

Listed:
  • Xue Zhang
  • Qing-ling Zhang
  • Zhongyi Xiang

Abstract

A singular prey‐predator model with time delays is formulated and analyzed. Allee effect is considered on the growth of the prey population. The singular prey‐predator model is transformed into its normal form by using differential‐algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. The existence of periodic solutions via Hopf bifurcation with respect to two delays is established. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold argument. Finally, numerical simulations are included supporting the theoretical analysis and displaying the complex dynamical behavior of the model outside the domain of stability.

Suggested Citation

Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:745296
DOI: 10.1155/2014/745296
as

Download full text from publisher

File URL: https://doi.org/10.1155/2014/745296
Download Restriction: no
File URL: https://libkey.io/10.1155/2014/745296?utm_source=ideas
LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
---><---

More about this item

Statistics

Access and download statistics

Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:745296. See general information about how to correct material in RePEc.

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

We have no bibliographic references for this item. You can help adding them by using this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1155/4058 .

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.