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The iodate–arsenous acid reaction was reported to be able to exhibit hysteresis bistability, including mushrooms and isolas, in a continuous flow stirred tank reactor (CSTR) when an additional flow of solvent is introduced [N. Ganapathisubramanian and K. Showalter, J. Chem. Phys. 80, 4177 (1984)]. Based on their kinetic data and the empirical rate law, it is shown that the reaction may also exhibit pitchfork-type and winged cusp-type singularities if additional flows of the reactants are introduced to the CSTR. [ABSTRACT FROM AUTHOR]

The idea ‘‘from bistability to oscillations,’’ originally proposed by De Kepper and Boissonade for studying and designing chemical oscillations, is extended to ‘‘from bistability to spatial pattern formation.’’ To carry out such extension, the idea from bistability to oscillations is discussed again by intuitive arguments based on the analysis of the intersection of the nullclines of kinetic equations and the linear stability analysis. By analogy between the kinetic equations of homogeneous reactions and the stationary equations of reaction–diffusion processes, similar intuitive arguments and linear stability analysis are applied to the reaction–diffusion equations, which leads to the conclusion that the homogeneous steady state being on the middle branch of the nullcline of the bistable subsystem is a necessary condition for spatial pattern formation. This condition becomes sufficient if the diffusion coefficients of the species involved in the feedback subsystem are much larger than those of the species which constitute the bistable subsystem. To demonstrate the validity of these conclusions, an example of heterogeneous catalysis system is studied analytically and numerically, and various temporal-spatial patterns, including the coexistence of a homogeneous steady state and an oscillating state or a spatial pattern, are revealed. The potential applications of the idea from bistability to spatial pattern formation to the experimental study and design of spatial patterns are discussed. [ABSTRACT FROM AUTHOR]

We study spatial pattern formation in surface-catalyzed reaction systems where products block active sites. We formulate a reaction-diffusion model that is based on Langmuir–Hinshelwood surface-reaction kinetics and on surface diffusion of the adsorbed species. Product occupancy is found to be a key element in the mechanism of spatial pattern formation. Numerical simulations show that such systems can exhibit multiplicity of stationary patterns, including the coexistence of a spatially homogeneous steady state and inhomogeneous stationary patterns. [ABSTRACT FROM AUTHOR]

A Langmuir–Hinshelwood-type model for isothermal reactions in small pellets of microporous solids can exhibit multiple steady states, oscillations, and coexistence of one oscillatory state with up to two stationary states, if blocking of active sites by the product is taken into account. [ABSTRACT FROM AUTHOR]

The statistical theory of solutions which provides a relation between chemical potentials and the composition fluctuations is extended to the nonequilibrium chemical reacting systems. The chemical potentials in nonequilibrium reacting systems are shown to be dependent not only on the concentrations, but possibly also explicitly on the nonequilibrium constraints acting on the system. Such dependence of chemical potentials on the nonequilibrium constraints may give the system a nonideal behavior, even though it was ideal at equilibrium. To characterize the dependence of nonidealities on the nonequilibrium extent, a nonequilibrium activity coefficient is formally defined and the quantitative dependences of nonequilibrium chemical potential and activity coefficient on the nonequilibrium extent are given for a simple reaction scheme. Some implications of such dependence to the chemical reaction and diffusion processes are discussed. [ABSTRACT FROM AUTHOR]

We develop a second-order response theory to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor. We apply the theory to the quadratic Schlögl model, a single-variable nonlinear reaction. In the presence of oscillating reactant or product concentrations or oscillating rate coefficients, the average intermediate concentration, the fluxes, and the dissipation are each a Lorentzian function of frequency with midpoint at the inverse relaxation time of the system. Thus even very short relaxation times can be determined by measuring average rates as a function of frequency of the perturbation. The amplitude of the Lorentzian depends on the chemical mechanism of the reaction and is proportional to the square of the amplitude of the applied perturbation. We also show that energy from the perturbation can be used to drive the reaction in a direction opposite of that predicted by the Gibb’s free energy difference of reactants and products, even under circumstances where the overall affinity is independent of the perturbation. [ABSTRACT FROM AUTHOR]

The Extended Brusselator is shown to contain Takens–Bogdanov bifurcation point, the location of which in parameter space is determined analytically. [ABSTRACT FROM AUTHOR]

It is shown that the Onsager reciprocal relations are satisfied in systems with multiple stationary states at equilibrium and the occurrence of complex dynamical phenomena such as chemical oscillation in nonideal systems close to equilibrium is not contradictory to linear irreversible thermodynamics. [ABSTRACT FROM AUTHOR]

A model, which is an extended version of the Brusselator, with additional steps Y <=>k C, is put forward to model the phenomena of multiple attractors. [ABSTRACT FROM AUTHOR]