Coexistence of multiple periodic and chaotic regimes in biochemical oscillations with phase shifts.

Abstract

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a multiplicity of stable coexisting states: birhythmicity, trirhythmicity, hard excitation and quasiperiodic with chaotic regimes. For different initial functions in the phase space one may observe the coexistence of two different quasiperiodic motions, the existence of a stable steady state with a stable torus, and the existence of a strange attractor with different stable regimes (chaos with torus, chaos with bursting motion, and chaos with different periodic regimes). For a single range of the control parameter values our system may exhibit different bifurcation diagrams: in one case a Feigenbaum route to chaos coexists with a finite number of successive periodic bifurcations, in other conditions it is possible to observe the coexistence of two quasiperiodicity routes to chaos. These studies were obtained both at constant input flux and under forcing conditions.