A chemostat with two organisms competing for a single growthlimiting nutrient controlled by feedback-mediated dilution rate is analyzed. A specific feedback function is constructed which yields circular and elliptical periodic orbits for the limiting system. A theorem on the stabilization of periodic orbits in conservative systems is developed and for a given elliptical orbit, the result is use...

Based on a master equation formalism for mesoscopic, unimolecular biochemical reactions, we show the periodic oscillation arising from severe nonequilibrium pumping is intimately related to the periodic motion in recently studied stochastic resonance (SR). The white noise in SR is naturally identified with the temperature in the biochemical reactions; the drift in the SR is associated with the ...

The study of the preimage problem of an endofunction on circular compositions is motivated by the study of coloring circular-arc graphs. In this paper we establish a 1-1 correspondence between preimages of a given circular composition S and proper S-sequences, and also provide a necessary and suucient condition for a sequence of subsets of the natural numbers to be a proper S-sequence for some ...