Types of oscillations in chemical reactions

Stable and Unstable Concentration Oscillations Induced by Temperature Oscillations on Reversible Nonequilibrium Chemical Reactions of Helicene Oligomers

Temperature oscillations can affect behaviors of living things. In this article, we describe the effect of triangle temperature oscillations on reversible nonequilibrium chemical reactions detected as concentration oscillations. When amplification through self-catalytic reactions is involved in the chemical reactions, concentration oscillations exhibit diverse nonequilibrium phenomena, which include equilibrium intersecting, equilibrium noncontact, and equilibrium sliding. Both stable and unstable concentration oscillations occur, during which repeated cycles provide the same and different concentration oscillations, respectively. Concentration oscillations are classified according to their waveforms in concentration/time profiles, the shapes of hysteresis curves in concentration/temperature profiles, the nature of self-catalytic reactions, and their relationships with equilibrium. An unstable concentration oscillation may be transformed into a stable concentration oscillation, which is described on the basis of the classifications. Experimental examples are shown using reversible association and dissociation reactions of helicene oligomers.

Sensitivity analysis of the noise-induced oscillatory multistability in Higgins model of glycolysis

A phenomenon of the noise-induced oscillatory multistability in glycolysis is studied. As a basic deterministic skeleton, we consider the two-dimensional Higgins model. The noise-induced generation of mixed-mode stochastic oscillations is studied in various parametric zones. Probabilistic mechanisms of the stochastic excitability of equilibria and noise-induced splitting of randomly forced cycles are analysed by the stochastic sensitivity function technique. A parametric zone of supersensitive Canard-type cycles is localized and studied in detail. It is shown that the generation of mixed-mode stochastic oscillations is accompanied by the noise-induced transitions from order to chaos.

Oscillatory Adsorption as the Determinant of the Fluctuating Behaviour of Different Heterogeneous Systems

Heterogeneous, catalytic oscillatory reactions as well as the oscillatory process of complex formation based on solid urea have been analysed in an attempt to ascertain the cause of such oscillatory mechanisms. In this context, oscillatory adsorption/desorption, phase transitions of the supported metal employed as the catalyst in the relevant oscillatory oxidation–reduction reactions as well as the reactions themselves have been considered.

Based on an analysis of two oscillatory systems, of which one (i.e. the oscillatory alkylation of isobutane with butenes on a metal-free zeolite catalyst) is not complicated by any phase transitions, whilst the other (i.e. the oscillatory formation of an urea–octane complex via the interaction of urea with a binary vapour mixture of octane and non-complex-forming hydrocarbons) is not complicated by any chemical reactions, it is possible to infer that the source of the oscillatory properties of heterogeneous systems which involve the chemical interaction of their components is oscillatory adsorption which occurs as an uncomplicated self-supporting process which appears to proceed without any increase in the entropy of the system.

The occurrence of oscillatory adsorption in a heterogeneous system leads to an oscillatory behaviour in the corresponding process, involving its simultaneous retardation in a similar manner as does the pendulum of a clock with respect to the untwisting of a spring or the oscillatory circuit of an electromagnetic system with respect to the discharge of a dry battery.

"Why not stoichiometry" versus "stoichiometry--why not?" Part I: General context

The elementary concepts involved with stoichiometry are considered from different viewpoints. Some examples of approximate calculations made according to the stoichiometric scheme are indicated, and correct resolution of the problems involved is presented. The principles of balancing chemical equations, based on their apparent similarities with algebraic equations, are criticized. The review concerns some peculiarities inherent in chemical reaction notation and its use (and abuse) in stoichiometric calculations that provide inconsistent results for various reasons. This "conventional" approach to stoichiometry is put in context with the generalized approach to electrolytic systems (GATES) established by Michałowski. The article contains a number of proposals that could potentially be taken into account and included in the next edition of the Orange Book. Notation of ions used in this article is not, deliberately, in accordance with actual IUPAC requirements in this respect. This article is intended to be provocative with the hope that some critical debate around the important topics treated should be generated and creatively expanded in the scientific community.

Boundedness of dynamical systems and chaos synchronization

Chaos synchronization in bounded dynamical systems is studied. We use boundedness of trajectories within the nonreplica approach to chaos synchronization and the Routh-Hurwitz criterion to propose a simple method to make negative conditional Lyapunov exponents. The method is tested on the classical Lorenz model.