Related papers: An analysis of indeterminate points in discrete in…
This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…
We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
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…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…