Quenching and revival of oscillations induced by coupling through adaptive variables

An adaptive coupling based on a low-pass filter (LPF) is proposed to manipulate dynamic activity of diffusively coupled dynamical systems. A theoretical analysis shows that tracking either the external or internal signal in the coupling via a LPF gives rise to distinctly different ways of regulating the rhythmicity of the coupled systems. When the external signals of the coupling are attenuated by a LPF, the macroscopic oscillations of the coupled system are quenched due to the emergence of amplitude or oscillation death. If the internal signals of the coupling are further filtered by a LPF, amplitude and oscillation deaths are effectively revoked to restore dynamic behaviors. The applicability of this approach is demonstrated in laboratory experiments of coupled oscillatory electrochemical reactions by inducing coupling through LPFs. Our study provides additional insight into (ar)rhythmogenesis in diffusively coupled systems.