In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random ne...

Biological processes are governed by complex networks ranging from gene regulation to signal transduction. Positive feedback is a key element in such networks. The regulation enables cells to adopt multiple internal expression states in response to a single external input signal. However, past works lacked a dynamical aspect of this system. To address the dynamical property of the positive feed...

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...

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...

It is proposed that any dynamical system with coexisting chaotic attractors has an emergent property. This provides a nonreductive explanation of mental states and their high sensitivity to noise and initial conditions. If metaphysical terms result from the mental states and these are emergent properties of dynamical systems with coexisting attractors, such as the brain, it is suggested that th...

Informally speaking, the Furstenberg Correspondence [5, 6] shows that the “local behavior” of a dynamical system is controlled by the behavior of sufficiently large finite systems. By the local behavior of a dynamical system (X,B, μ,G), we mean the properties which can be stated using finitely many actions of G and the integral given by μ1. By a finite system, we just mean (S,P(S), c, G) where ...

In a companion paper [Q. Hui, W.M. Haddad, Semistability of switched dynamical systems. Part I: Linear system theory, Non-linear Anal. Hybrid Syst. 3 (3) (2009) 343–353] semistability and uniform semistability results for switched linear systems were developed. In this paper we develop semistability analysis results for non-linear switched systems. Semistability is the property whereby the solu...

We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset) the state based on a linear affine map. In particular, we consider two families of discrete events, with the first family of resets occurring at exponentiall...

We give a precise non trivial counterexample to the existence of the Møller morphism for groups of *-automorphism describing a two-body interacting dynamical system. This fact invalidate the property of L1 asymptotic abelianness which is a crucial ingredient in many developments of the non-stationary approach on the stability of KMS states. It is build on the spin fermion dynamical system, neve...