M. Marek

Experimental observations of periodic and chaotic regimes in a forced chemical oscillator

Abstract Experiments showing periodic and chaotic behavior in a Belousov-Zhabotinski (Bue5f8Z) reaction mixture in a stirred flow reactor with periodic addition of bromide ions are presented. An alternating sequence of periodic and aperiodic regimes as a function of the period of Br - pulses is observed in experiments. This behavior is well described by a simple model based on the results of single-pulse experiments.

Dynamic regimes in a periodically forced reaction cell with oscillatory chemical reaction

Abstract Periodic and aperiodic regimes in a forced chemical system are studied experimentally and the observations are interpreted on the basis of phase transition curves evaluated both from the model equations and experimentally. The periodically oscillating system of the Belousov-Zhabotinski reaction in a flow-through stirred reaction cell exhibited phase transition curves both of the type 1 and 0 when a single pulse perturbation by bromide ions was used. This behaviour is only partly described by the mathematical models studied. Phase synchronization, intermittency and chaos were observed when the frequency and amplitude of concentration perturbations were varied in continuous forcing experiments. A one-dimensional deterministic model based on the experimental phase curves describes results of continuous forcing relatively well; better agreement was reached when effects of experimental noise were included in the model.

Resonance behaviour in two-parameter families of periodically forced oscillators

Abstract We study resonance (periodic) behaviour in two-dimensional autonomous oscillators, periodically forced by discrete jumps in state space. Two different models are examined numerically using continuation methods. The results are qualitatively similar in both cases and show that regions of various resonances are bounded in the forcing-amplitude-forcing-period parameter plane and have a rich internal bifurcation structure.

Reduction waves in the BZ reaction: circles, spirals and effects of electric field

Abstract Spatiotemporal patterns in the Belousov-Zhabotinsky reaction medium in a Petri dish at low concentrations of malonic acid are studied experimentally and theoretically. Depending on the concentration of malonic acid, the interaction of reduction and oxidation front waves may lead to: (i) a disappearing reduction pulse wave, (ii) complex target structures, (iii) a stably propagating reduction pulse wave. A mechanical perturbation can lead either to reduction spirals or to healing effects causing heart-shaped structures. Imposed electric field causes a symmetry breaking of target patterns and can stabilize or destabilize the waves. A formal reaction-diffusion model reproduces qualitatively most of the experimentally observed phenomena in the absence of electric field. A modified Oregonator model that involves ionic migration describes well some experiments including those in the presence of electric field.

Excitable Chemical Reaction Systems

Well defined and thoroughly studied chemical reaction systems such as the Belousov-Zhabotinskii (BZ) reaction [4] often enable a comparison of experimental results with the results of modelling both in oscillatory and excitable systems [2, 5, 8]. In this paper we make an attempt to demonstrate that properties of distributed forced excitable BZ systems can be understood on the basis of the response of the corresponding lumped parameter system (CSTR) to a single or periodic pulse forcing. We introduce an experimental technique for the construction of the phase excitation curve (PEC), based on double pulse experiments and demonstrate its use for the modelling and interpretation of the dynamical response of excitable systems to external forcing.

Pulse Stimulation of Coupled Chemical Oscillators

Stimulated single and coupled reaction cells serve as well defined models of behaviour of dynamical regimes of biological cells and tissues. Results of experimental and theoretical studies of responses to single and periodic pulse stimulations of an oscillating open (flow-through) reaction cell were discussed in earlier papers [1, 2]. It was demonstrated that single pulse stimulation can cause both positive and negative phase shift of concentration oscillations. The phase transition curves (PTC), i.e. The dependence of the new (shifted) phase of the oscillation on the phase when the stimulation has been applied, were constructed from experimental data. For strong stimulations PTC s were of the topological type “0” and for weak stimulations of the type “1” [2].

Dynamic Patterns in Interacting Chemical Cells and Effects of External Periodic Forcing

Chemical reactions with nonlinear kinetics serve as model systems for the study of nonlinear dynamics /1/. Periodic, quasiperiodic and chaotic oscillations are observed in a flow-through well-stirred reaction cell /2/. A large number of dynamic systems are modelled as a set of oscillating units with mutual interaction. The interaction is one-directional in a special case of periodically forced systems. Well-stirred flow-through reaction cells with an oscillating chemical reaction and mutual mass exchange and/or external concentration periodic forcing serve as a convenient model system /3–6/ with a number of analogies, for example, to biological cell structures. The Belousov-Zhabotinsky reaction /7/ is most often used as a source of oscillations in a single reaction cell.