\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Stability, delay, and chaotic behavior in a Lotka-Volterra predator-prey system

Abstract Related Papers Cited by
  • We consider the following Lotka-Volterra predator-prey system with two delays:
    $x'(t) = x(t) [r_1 - ax(t- \tau_1) - by(t)]$
    $y'(t) = y(t) [-r_2 + cx(t) - dy(t- \tau_2)]$ (E)
    We show that a positive equilibrium of system (E) is globally asymptotically stable for small delays. Critical values of time delay through which system (E) undergoes a Hopf bifurcation are analytically determined. Some numerical simulations suggest an existence of subcritical Hopf bifurcation near the critical values of time delay. Further system (E) exhibits some chaotic behavior when $tau_2$ becomes large.
    Mathematics Subject Classification: 34D35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(68) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return