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The computer-aided bifurcation analysis of predator-prey models. (English) Zbl 0547.92015
Summary: Mathematical analysis of dynamical systems can often benefit from companying numerical computations. This is particularly true if one has software capable of providing an automatic bifurcation analysis of such systems. Computer programs of this type now exist.
We describe the application of such software to a predator-prey model. Phenomena that arise in this analysis include stationary bifurcations, limit points, Hopf bifurcations and secondary periodic bifurcations. A two-parameter numerical analysis leads quite naturally to the detection of higher order singularities.

MSC:
92D25 Population dynamics (general)
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65-04 Software, source code, etc. for problems pertaining to numerical analysis
37-XX Dynamical systems and ergodic theory
92-04 Software, source code, etc. for problems pertaining to biology
Software:
AUTO; COLSYS
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