Two-parameter stochastic resonance in the absence of external signal for the photosensitive Belousov–Zhabotinsky reaction

The Tris(2,2'-Bipyridyl)Ruthenium-Catalysed Belousov–Zhabotinsky Reaction

The Belousov – Zhabotinsky (BZ) reaction is the prototypical oscillating chemical reaction. The tris(2,2'-bipyridine)ruthenium-catalysed BZ reaction (often simply referred to as the ruthenium-catalysed BZ reaction) displays photosensitivity and has been widely exploited for examination of the effects of illumination on nonlinear reaction kinetics. In this review, we investigate the behaviour of the ruthenium-catalysed BZ reaction. The mechanism of the reaction is analysed and we examine how light sensitivity is incorporated into kinetic models of the reaction. The temporal dynamics of the photosensitive reaction is presented and, finally, we discuss the extraordinary wealth of behaviour that has been observed in the spatially-distributed system when perturbed by visible light.

Effective phase dynamics of noise-induced oscillations in excitable systems

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.

Internal stochastic resonance under two-parameter modulation in intercellular calcium ion oscillations

Internal stochastic resonance (ISR) in a model of intercellular calcium ion oscillations is investigated under the modulation of two parameters, viz., degree of extracellular stimulation (beta) and leak rate (k(f)). ISR can occur when either beta or k(f) is subjected to a noise. Internal stochastic biresonance (ISBR) can occur when noise is added to the two parameters simultaneously. The distance to the bifurcation point is found to be able to enhance or suppress the ISBR, and to affect the number of peaks of ISR.

Experimental observation of coherence resonance in an excitable chemical reaction system

Dynamics of an excitable Belousov-Zabotinsky reaction system under an external noise are investigated using cation exchange beads loaded with the cationic catalyst. When a noise amplitude is increased above a certain value, an oscillatory state appears. It is shown that the coherence of these noise-excited oscillations is maximal for a suitable value of the noise amplitude. This phenomenon is characterized by using various statistical measures, such as the signal-to-noise ratio in the power spectrum, the correlation time of the noise-excited oscillation, and the standard deviation of time intervals between successive firing events. We find the experimental evidence that the period of coherent oscillation is determined by a characteristic time scale of the system.

Stochastic resonance in delayed two-coupled oscillators without common perturbations

Stochastic resonance (SR) in a two-coupled oscillator system with time delay is investigated. The system shows multistability of a desynchronized state and two synchronized states with different collective frequencies, which may be interpreted as multistable perception of ambiguous or reversible figures. To model the situations where the two oscillators exist in different environments, periodic signals and noises at their inputs are not uniformly given. SR in an individual oscillator, characterized by the output signal-to-noise ratio, is examined based on numerical simulations. We find that phase shift between the signals at inputs of different oscillators weakens SR, the oscillator with only an input signal does not show SR, and the oscillator with input noise shows SR irrespective of it having an input signal or not. The results have implications in the area of information transmission in biological systems.