A class of Pyragas type nonlocal feedback controllers with timedelay is investigated for the Schlögl model. The main goal is to find an optimal kernel in the controller such that the associated solution of the controlled equation is as close as possible to a desired spatio-temporal pattern. An optimal kernel is the solution to a nonlinear optimal control problem with the kernel taken as control...

An open flow bistable Schlögl model in a well-stirred isothermal reaction volume V showing the balance of entropy production and exchange on non-equilibrium stationary states.

the cellular automata method has been used to simulate the pattern formation of the schlögl model as a bistable reaction-diffusion system. both microscopic and macroscopic cellular automata approaches have been considered and two different methods for obtaining the probabilities in the microscopic approach have been mentioned. the results show the tendency of the system towards the more stable ...

Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatiotemporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time, and correlation length appear explicitly. The different effects of these parameters are discussed for the Ginzburg-Landau and Schlögl models. We obtain an analy...

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctu...

A high activity of reactions can be confined in a model cell with a semipermeable membrane in the Schlögl model. It is interpreted as a model of primitive metabolism in a cell. We study two generalized models to understand the creation of primitive cell systems conceptually from the view point of the nonlinear-nonequilibrium physics. In the first model, a single-cell system with a highly active...