Chaos theory in chemistry and chemometrics: a review

Abstract

Since the initial development of chaos theory and corollary concepts such as the strange attractor and fractal dimensionality, there has been a nontrivial effort to apply these concepts to the quantification of material and data structures. There exists within chaos theory modeling concepts that allow for thorough complexity analyses not available through alternate paradigms. The purpose of this paper is to review the main body of work that has been pursued in both experimental chemistry research and related data analysis development with respect to chaos theory and derivative ideas.

Six questions on topology in theoretical chemistry

“…As non exhaustive examples: graph theory has been applied to molecular structure, dynamical system theory (enabling to extract qualitative pieces of information from numbers) to the study of different scalar fields (BO energy surfaces, electron density, MESP, ELF), knot theory to the study of chirality, fractal theory to colloïds and dendrimers, chaos theory to oscillating reactions. Interesting reviews have been written by Babaev [2] and Cramers [3].…”

“…Secondly, the other big area is that the interpretation and rationalisation of traditional chemistry, as a "single-molecule science", which needs to be revisited and "cleaned up". For example, textbooks do not explain satisfactorily [92] why the B−F bond length is so short in BF 3 . A minimally constructed topological electronegativity scale (without the assumptions [93] of the Electronegativity Equalisation Method or any other framework), is also highly desirable.…”

Fractal nature of protein surface roughness: a note on quantification of change of surface roughness in active sites, before and after binding

“…A recent study applied this idea to the study of the fractal nature of proteins at different aggregate scales (Lahiri et al ., ). For a little technical discussion on the various multifractal methodologies, one can refer to the work of Cramer and Booksh (). However, drawing upon percolation‐driven investigations, another recent work argued that multifractality of proteins may be better approximated by single, local FDs (Antal et al ., ).…”

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

“…This myth vanished in 1983 thanks to Yamada and Fujisaka [6] where a methodology for the synchronization of two chaotic systems using bidirectional coupling is presented, meanwhile in 1990 Pecora and Carroll [7] proposed the synchronization of the drive and response systems with different initial conditions. Since then, a wide series of alternative methodologies for the synchronization of chaotic systems have been developed [8][9][10][11][12][13][14][15][16] and thanks to this methodologies, a vast quantity of possible applications have been found in science and engineering, from physics [17,18], optics [19,20], biology [21][22][23], chemistry [24,25] and specially in the branch of secure communications [26][27][28].…”