Continuous Coupling of Chaotic and Periodic States of Chemical Oscillators With and Without Time Delay

Abstract

AbstractWe present continuous coupling experiments and calculations of two mutually flow‐rate‐coupled Belousov‐Zhabotinsky (BZ) oscillators. The Ce4+‐concentration of one BZ‐reactor controls the flow rate into the other BZ‐reactor and vice versa. Flow‐rate control is proportional to the difference between the (time delayed) Ce4+‐and an average Ce4+‐concentration. When both period one (P1) BZ oscillators are weakly coupled, the P1 oscillations are retained in both oscillators whose periods increase with increasing coupling strength. At high coupling strengths statistically aperiodic oscillations are produced. The introduction of time delayed coupling does not reduce the noise in the strongly coupled system. We distinguish between statistical aperiodicity due to experimental noise and deterministic chaos due to the system's nonlinear dynamics. At constant coupling strength a rising delay time produces a “sawtooth” like behaviour of the P1 periods. Mutual flow‐rate‐coupling of two chaotic states without time delay retains chaos in both reactors at low coupling strengths. When the coupling strength increases the Hausdorff dimension passes through a maximum (≈︁ 2.5). At very high coupling strengths, a transition from chaos to periodic states takes place.