Related papers: Chaotic behavior of the $P$-adic Potts-Bethe mappi…
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also…
We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange…
A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures which make use of Pade approximants and interpolating exponentials to both…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
The main subject to study in this paper are properties of the sequence of reversely iterated segments. Especially, we will examine properties of chaotic behavior of the sequence of measures of corresponding segments. Our results are not…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Randomly coupled neural fields demonstrate chaotic variation of firing rates, if the coupling is strong enough, as has been shown by Sompolinsky et. al [Phys. Rev. Lett., v. 61, 259 (1988)]. We present a method for reconstruction of the…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
The onset of chaos and the mechanism of rotational damping are studied in an exactly soluble particle-rotor model. It is shown that the degree of chaoticity as inferred from the statistical measures is closely related to the onset of…
This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We discuss various numerical approaches for studying the chaotic dynamics of multidimensional Hamiltonian systems, focusing our analysis on the chaotic evolution of initially localized energy excitations in the disordered Klein-Gordon…