Related papers: Analytical Approach for Piecewise Linear Coupled M…
We provide a detailed discussion about the unitary and reduced evolution induced by family of Hamiltonian models describing a multilevel system, with a ground state and a possibly multilevel excited sector, coupled to a multimode boson…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
We study the continuum space-time limit of a periodic one dimensional array of deterministic logistic maps coupled diffusively. First, we analyse this system in connection with a stochastic one dimensional Kardar-Parisi-Zhang (KPZ) equation…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…
Canonical paths is one of the most powerful tools available to show that a Markov chain is rapidly mixing, thereby enabling approximate sampling from complex high dimensional distributions. Two success stories for the canonical paths method…
Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables…
We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+\overline g \colon \D\to\C \] such that \[ |g'(z)|\le k|h'(z)|,\qquad z\in\D, \] while the analytic part \(h\) is unbounded. The construction is based…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
Phase transitions of the mixed spin-1/2 and spin-S (S >= 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple…
In the field of the Jacobian conjecture it is well-known after Druzkowski that from a polynomial "cubic-homogeneous" mapping we can build a higher-dimensional "cubic-linear" mapping and the other way round, so that one of them is invertible…
We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest…
We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant…
For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce…
We extend the conductance and canonical paths methods to the setting of general finite Markov chains, including non-reversible non-lazy walks. The new path method is used to show that a known bound for mixing time of a lazy walk on a Cayley…
Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence.…