Neurons modeled by the Rulkov map display a variety of dynamic regimes that include tonic spikes and chaotic bursting. Here we study an ensemble bursting neurons coupled with Watts-Strogatz small-world topology. We characterize sequences bursts using symbolic method time-series analysis known as ordinal analysis, which detects nonlinear temporal correlations. show probabilities different symbol...

We study the family of the Lozi maps La,b : R2 → R2, La,b(x, y) = (1+y−a|x|, bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches. 2010 Mathematics Subject Classification: 37B10, 37D45, 37E30, 54H20

This letter shows some counter-intuitive simulation results that the symbolic sequences and the state variables of a digital filter with two’s complement arithmetic and arbitrary initial conditions and order will be eventually zero when all the filter parameters are even numbers, no matter the system matrix of the filter is stable or not.

Transition patterns between different sleep stages are analysed in terms of probability distributions of symbolic sequences for young and old subjects with and without sleep disorder. Changes of these patterns due to ageing are compared with variations of transition probabilities due to sleep disorder.

Here expounded is a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalization, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed. AMS Subject Classification: 41A58, 41A80, 65B10, 05A15, 33C45, 39A70.

this article reviews the ancient symbolic world, shia and modernity believes in iranian’s mind which are historical link between ancient symbolic world and shie. since the late nineteenth century with the modernization, for exampel civilization, constitutional movement and palavi government, gap created in iranians mind. dispite this gap, iranians mind have symbolic characteristics and are not ...

We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex dynamics regularities and patterns emerge. 1 Symbolic dynamics distinguishing chaotic from random dynamics 1.1 Random sequences and dynamical iterates Accordin...

We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-...

Data-driven systems are gathering increasing amounts of data from users, and sensitive user requires privacy protections. In some cases, the gathered is non-numerical or symbolic, conventional approaches to privacy, e.g., adding noise, do not apply, though such still require Accordingly, we present a novel differential framework for protecting trajectories generated by symbolic systems. These c...