Why do rodent populations fluctuate? stability and bifurcation analysis of some discrete and continuous predator-prey models

Abstract: A review of the microtine rodent cycle problem is given as well as a review of mathematical results related to the microtine rodent cycle problem. Biologically, 1 treat dynamical consequences of generalist predation and optimal breeding behavior. Mathematically, I emphasize especially the problems of global stability and uniqueness of limit cycles for ordinary differential equations. These problems are related to the famous Hilbert's 16th problem, part b. Since it is not evident how to model microtine rodent cycles, continuous as well as discrete dynamical systems and their relations are treated.