In this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology. The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial gr...

Oscillating reactions are one of the most interesting topics in chemistry and analytical chemistry. Fluctuations in concentrations of one the reacting species (usually a reaction intermediate) create an oscillating chemical reaction. In oscillating systems, the reaction is far from thermodynamic equilibrium. In these systems, at least one autocatalytic step is required. Developing an instinctiv...

The autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as an extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with changes of the system size and flow is studied, while a...

We investigate the effects of hyperbolic hydrodynamical mixing on the reaction kinetics of autocatalytic systems. Exact results are derived for the two dimensional open baker map as an underlying mixing dynamics for a two-component autocatalytic system, A + B → 2B. We prove that the hyperboliticity exponentially enhances the productivity of the reaction which is due the fact that the reaction k...

In this paper, we show experimentally that inside a microfluidic device, where the reactants are segregated, the reaction rate of an autocatalytic clock reaction is accelerated in comparison to the case where all the reactants are well mixed. We also find that, when mixing is enhanced inside the microfluidic device by introducing obstacles into the flow, the clock reaction becomes slower in com...

An autocatalytic reaction in which the reaction product serves as a catalyst to produce more of itself and to suppress production of its enantiomer serves as a mechanistic model for the evolution of homochirality. The Soai reaction provided experimental confirmation of this concept, nearly 50 years after it was first proposed. This Perspective offers a rationalization of the Soai autocatalytic ...