\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2010, Volume 14, Issue 1: 233-250. Doi: 10.3934/dcdsb.2010.14.233
This issue Previous Article Infinite sum of the product of exponential and logarithmic functions, its analytic continuation, and application Next Article Symmetrical solutions of backward stochastic Volterra integral equations and their applications

The saddle-node-transcritical bifurcation in a population model with constant rate harvesting

  • 1.

    Faculty of Sciences and Mathematics, Universitas Pelita Harapan, Jl. M.H. Thamrin Boulevard, Tangerang, 15811

  • 2.

    Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St. N., L1H 7K4 Oshawa, Ontario

  • 3.

    Department of Mathematics and Statistics, La Trobe University, Victoria 3086

Received:  March 31, 2009
Revised:  February 28, 2010
Published:  June 2010
Abstract Related Papers Cited by
    Abstract
  • We study the interaction of saddle-node and transcritical bifurcations in a Lotka-Volterra model with a constant term representing harvesting or migration. Because some of the equilibria of the model lie on an invariant coordinate axis, both the saddle-node and the transcritical bifurcations are of codimension one. Their interaction can be associated with either a single or a double zero eigenvalue. We show that in the former case, the local bifurcation diagram is given by a nonversal unfolding of the cusp bifurcation whereas in the latter case it is a nonversal unfolding of a degenerate Bogdanov-Takens bifurcation. We present a simple model for each of the two cases to illustrate the possible unfoldings. We analyse the consequences of the generic phase portraits for the Lotka-Volterra system.
    Mathematics Subject Classification: Primary: 37H20, 37L10, 37N25.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(780) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences