Stability and bifurcation analysis for a delayed Lotka–Volterra predator–prey system. (English) Zbl 1095.92071

Summary: The present paper deals with a delayed Lotka-Volterra predator-prey system. By linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation, we find necessary conditions that the parameters should verify in order to have oscillations in the system. In addition, the normal form of the Hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these Hopf bifurcations. To verify the obtained conditions, a special numerical example is also included.


92D40 Ecology
34K18 Bifurcation theory of functional-differential equations
37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
37N25 Dynamical systems in biology
34K13 Periodic solutions to functional-differential equations
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