The qualitative behavior of coupled predator-prey oscillations as deduced from simple circle maps

Qualitative patterns of the non-equilibrium behavior of coupled consumer/resource systems, formulated as a standard circle map, are explored. Patterns of demographic locking, reflected as a "devil's staircase", are observed in simulations of the MacArthur consumer/resource equations. As coupling strength increases the steps in the staircase become broader, eventually overlapping to form a chaotic pattern. In addition to the standard form of chaos formation from overlapping Arnold tongues, a pattern of period doubling in the non-invertible standard circle map corresponds to the pattern observed in the classic consumer/resource equations.