Synchronization by irregular inactivation

Transient resetting: a novel mechanism for synchrony and its biological examples

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in the medical therapy of rhythmic disorders. Examples of the synchronization of neural and circadian oscillators as well as a chaotic neuron model are presented to verify our hypothesis.

Synchronization of dynamical systems is a process whereby two or more systems adjust a given property of their motions to a common behavior due to coupling or forcing. Synchronization has attracted much attention from physicists, biologists, applied mathematicians, and engineers for many years and is a ubiquitous phenomenon. In this paper, Li et al. present a very simple, but general mechanism, called transient resetting, that explains stimulus-induced synchronization in dynamic systems. The mechanism pertains not only to periodic oscillators but also to chaotic ones, and not only to continuous time systems but also to discrete time systems. Biological systems are dynamic, and their synchronization is essential, for example, in the genesis of rhythmic phenomena and information processing. In this paper, the authors study several possible instances of their novel mechanism in a biological context. They also suggest that transient resetting might be used therapeutically in rhythmic disorders. The beneficial role of noise in biological systems has been studied extensively in recent years. Li and colleagues' mechanism provides an explanation for this role in the synchronization in biological systems, even when the stimulus or input to the system is not random or noisy.

Collective reaction behavior of an oscillating system coupled with an excitable reaction

The collective reaction behavior of limit cycles coupled to a nonoscillatory forcing is investigated experimentally and computationally. The coupled chemical system is constructed by adding 1,4-cyclohexanedione (CHD), a species which is capable of forming an oscillator with acidic bromate, into the cerium-catalyzed Belousov-Zhabotinsky reaction. Two levels of coupling exist in the system: (1) through autocatalytic reactions with bromine dioxide radicals and (2) via reactions with oxidized metal catalysts. Experiments illustrate that there is an optimum [1,4-CHD]/[cerium] ratio for inducing complex oscillations, whereas in the 1,4-CHD and malonic acid concentration phase plane two resonant ratios are observed for the onset of complex behavior. In addition, bromate, the oxidant for both suboscillators, also exhibits subtle influences on the complexity of the collective reaction behavior. The experimental observations are qualitatively reproduced with the Field-Koros-Noyes mechanism, modified to account for the coupling reactions with the 1,4-CHD-bromate system.

Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox

We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox.

External noise synchronizes forced oscillators

Periodic pulsatile perturbation of nonlinear oscillators generates phase-locking, quasiperiodic, and chaotic responses. This work shows that the application of external noise to ensembles of such forced systems can synchronize oscillations, even in regimes where neither the noise nor the periodic forcing, when applied alone, would lead to such a phenomenon.