Related papers: Dynamical systems on chain complexes and canonical…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force…
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…
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and…
For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
A dynamical system is a pair $(X,f)$, where $X$ is a topological space and $f\colon X\to X$ is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems,…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…