Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemi...

Abstract. Optimal sparse control problems are considered for the FitzHugh-Nagumo system including the so-called Schlögl model. The non-differentiable objective functional of tracking type includes a quadratic Tikhonov regularization term and the L1-norm of the control that accounts for the sparsity. Though the objective functional is not differentiable, a theory of second order sufficient optim...

The importance and different aspects of autocatalysis in evolution was analyzed. The behaviour of autocatalytic reactions mainly the Lotka-Volterra and the Schlögl equations were discussed in terms of phase change, entropy, and their oscillation frequency. The increase of complexity as the general direction of evolution was examined on some patterns in terms of both their entropy and informatio...

Inside Cover: In article 2200586, Sandra Schlögl and co-workers demonstrate that Acrylate functional coumarin monomers are synthetized cured by wavelength orthogonal photoreactions yielding soft (405 nm) stiff (365 networks. Advancing from thin films, the dual 3D printing of active devices is demonstrated with locally controlled mechanical thermal properties using a single vat. The concept high...

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schlögl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing...

We investigate the problem of sparse optimal controls for the so-called Schlögl model and the FitzHugh-Nagumo system. In these reaction-diffusion equations, traveling wave fronts occur that can be controlled in different ways. The L-norm of the distributed control is included in the objective functional so that optimal controls exhibit effects of sparsity. We prove the differentiability of the ...

The behaviour of a class of autocatalytic systems with intermediates has been studied. A general chemical model has been derived, and the corresponding kinetic differential equations have been studied by both analytical and numerical methods. Two special cases were investigated in more detail: a competitive model, closely related to the second order Schlögl model, and a mutualistic model, deriv...

The stabilizability to trajectories of the Schlögl model is investigated in norm natural state space for strong solutions, which strictly contained standard pivot square integrable functions. As actuators a finite number indicator functions are used and control input subject bound constraint. A stabilizing saturated explicit feedback proposed, where set independent targeted trajectory. Further,...

Ternary and quaternary Cr or Ga-containing ex-LDH catalysts influence of the additional oxides onto the microstructure and activity of Cu/ZnAl2O4 catalysts Stefanie Kühl, Julia Schumann, Igor Kasatkin, Michael Hävecker, Robert Schlögl, Malte Behrens* Fritz-Haber-Institut der Max-Planck-Gesellschaft, Department of Inorganic Chemistry, Faradayweg 4-6, 14195 Berlin, Germany; Max-Planck-Institute f...