Related papers: Mapping dynamical systems into chemical reactions
Three-dimensional polynomial dynamical systems (DSs) can display chaos with various properties already in the quadratic case with only one or two quadratic monomials. In particular, one-wing chaos is reported in quadratic DSs with only one…
A number of simple chaotic three-dimensional dynamical systems (DSs) with quadratic polynomials on the right-hand sides are reported in the literature, containing exactly 5 or 6 monomials of which only 1 or 2 are quadratic. However, none of…
We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The…
This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: Establish a…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good…
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a…
We present an extensive introduction to quantum collision models (CMs), also known as repeated interactions schemes: a class of microscopic system-bath models for investigating open quantum systems dynamics whose use is currently spreading…
Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using…
The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible…
Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states…