Introduction to the dynamic self-organization of chemical systems: Part I: Basic concepts and techniques of nonlinear dynamics in chemistry

• Published in: ChemTexts (Cham) 2017-09, Vol.3 (3), Article 12
• Main Author: Orlik, Marek
• Format: Article
• Language: English
• Subjects: Biochemistry; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Environmental Chemistry; Lecture Text
• ISSN: 2199-3793; 2199-3793
• DOI: 10.1007/s40828-017-0049-5

Classical education in chemistry rarely includes the characteristics of dynamic phenomena that are the basis for understanding of nonequilibrium self-organization of matter. In the oscillatory course of such processes, the concentrations of the intermediates or the electric current/electrode potential vary in time in a periodic manner, often with the stunning visual effect. In inhomogeneous systems, where the transport processes are combined with the nonlinear reaction kinetics, spatiotemporal patterns can also emerge. Moreover, such systems can exhibit excitability, i.e., amplified excitation occurring only upon certain threshold perturbation, like for neurons. Finally, chemical systems can be multistable, i.e., exhibit more than one stable state for the same control parameters. In all these phenomena, the decrease in entropy related to the emergence of order is compensated by the entropy production in the dissipative process. From the kinetic point of view, for the self-organization to occur, the dynamics of the system must be nonlinear and include feedback loops. Then omnipresent fluctuations are no longer damped but amplified, giving rise to macroscopic patterns. To recognize these common features of different real systems revealing such complex temporal or spatiotemporal dynamics, it is instructive to construct their kinetic and mathematical models revealing the respective bifurcations—the qualitative changes in the system’s state upon variation of the control parameters. These bifurcations can be diagnosed, e.g., with linear stability analysis. The course, designed essentially for graduate students, is divided into two parts: I. Basic concepts and techniques of nonlinear dynamics in chemistry and II. Dynamic instabilities in selected chemical systems.