Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...

Resynchronizing dynamical systems are important for certain chaotic signal masking methods. We demonstrate the dependence of the resynchronizing property of linear dynamical systems on choices of coordinate systems. Using these insights, we demonstrate how a nonlinear system not previously known to be synchronizable can be used for chaotic signal masking.

In this paper, we investigate the application of non-local graph entropy in evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement–decay graph dynamics, which leads to scale-free graphs. We find that the node entropy cha...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

discrete iterated function systems discrete iterated function systems representation of discrete sequences with dimensional discrete iterated function systems discrete iterated function systems stochastic discrete scale invariance: renormalization representation of discrete sequences with high-dimensional power domains and iterated function systems fractal tilings from iterated function systems...

For a compact metric space ∆ we consider the compact space S(∆) of shift-invariant subsystems of the full shift ∆, endowed with the Hausdorf metric.. We show that when ∆ is perfect the space S(∆) and the homeomorphism group Homeo(K) of the Cantor set (with the topology of uniform convergence) are topologically generically equivalent in the sense of Glasner and King [7], ie a dynamical property ...

Living systems are embedded within physical space. While this embedding can be viewed as a restrictive constraint on structure, where the prohibitive costs of establishing or maintaining interactions over long distances mitigate against certain kinds of potential organisation, it can also be seen as an enabling factor, bringing about correlations, regularities and symmetries that can be exploit...

It is shown using Lund Monte Carlo that, unlike the average properties of the hadronic system inside jets, the anisotropy of dynamical fluctuations in these systems changes abruptly with the variation of the cut parameter ycut. A transition point exists, where the dynamical fluctuations in the hadronic system inside jet behave like those in soft hadronic collisions. Thus the anisotropy property...

THEOREM. In order that a system S of o I curves represents the additivemultiplicative trajectories ofa given field, it is necessary (but not sufficient) that S possesses the dynamical Property I; this may be stated simply in either of these alternative geometric forms: Property Ia: For the o I curves of S passing through any lineal element E of the plane, construct the osculating parabolas at E...