To be Announced.

To be Announced.

Nonequilibrium coexistence through strange periodic attractors.

Strange periodic attractors with complicated, long-lasting transient dynamics are found in a prey-predator model with disease transmission in the prey. The model describes viral infection of a phytoplankton population and grazing by zooplankton. The analysis of the three-dimensional system of ordinary differential equations yields several (semi-)trivial stationary states. Nontrivial equilibria only exist in form of a continuum line when a particluar parameter combination is met. However, more realistic to occur in nature is the emergence of a strange periodic attractor, stabilizing itself after a repeated torus-like oscillation. We will point out similarities of this form of coexistence with persistence and permanence in ecological communities as well as with electrical bursting phenomena in physiology.

This is joint work with Horst Malchow (University of Osnabrueck, Germany).

Keywords: Strange periodic attractor, predation, viral plankton infection, fold-Hopf (zero-pair) bifurcation, zip bifurcation, permanence.

Microbial Population Genetics.

Not supplied.