Chaotic oscillations and cycles in multi-trophic ecological systems

A set of multi-trophic population models are described, all of which yield an interesting form of chaotic dynamics—namely, the populations cycle in a periodic fashion, yet the peak abundance within each cycle is erratic and irregular over time. Since there are many ecological and biological systems that are characterized with this same form of “uniform phase-growth and chaotic amplitude (UPCA),” these models should be useful in a range of applications. We discuss their relevance to the well-known Canadian hare-lynx system, and other small mammal foodwebs which together comprise wildlife's unusual “four and ten year cycle.” The dynamics of the model equations are analysed and an explanation is given as to the source of the UPCA dynamics in the new class of foodweb systems presented, and in others found in the literature.