Results 1 
7 of
7
A nonlinear dynamics perspective of Wolfram’s new kind of science. Part III: Predicting the unpredictable
 International Journal of Bifurcation and Chaos
, 2004
"... This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justi ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenomena is that it is based on concepts from nonlinear dynamics and attractors where many fuzzy concepts introduced by Wolfram via brute force observations can be defined and justified via mathematical analysis. The main result of Part I is the introduction of a fundamental concept called linear separability and a complexity index κ for each local Rule which characterizes the intrinsic geometrical structure of an induced “Boolean cube ” in threedimensional Euclidean space. In particular, Wolfram’s seductive idea of a “threshold of
Intelligence and Cooperative Search by Coupled Local Minimizers
, 2001
"... this paper we propose a new methodology of coupled local minimizers (CLM) for solving continuous nonlinear optimization problems. We pose a somewhat similar challenge as for committee networks but within a di#erent and broader context of solving di#erentiable optimization problems. The aim is to (on ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
this paper we propose a new methodology of coupled local minimizers (CLM) for solving continuous nonlinear optimization problems. We pose a somewhat similar challenge as for committee networks but within a di#erent and broader context of solving di#erentiable optimization problems. The aim is to (online) combine the results from local optimizers in order to let the ensemble generate a local minimum that is better than the best result obtained from all individual local minimizers. We show how improved local minima can be obtained by having interaction and information exchange between the local search processes. This is realized through state synchronization constraints that are imposed between the local minimizers by incorporating principles of masterslave dynamics. Synchronization theory has been intensively studied within the area of chaotic systems and secure communications [Chen & Dong, 1998; Pecora & Carroll, 1990; Suykens et al., 1996, 1997, 1998; Wu & Chua, 1994]. The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems. CLMs also fit within the framework of Cellular Neural Networks (CNN) [Chua & Roska, 1993; Chua et al., 1995; Chua, 1998]. By considering the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints, a continuoustime optimization algorithm is studied according to Lagrange programming networks [Cichocki & Unbehauen, 1994; Zhang & Constantinides, 1992]. The resulting continuoustime optimization algorithm is described by an array of coupled nonlinear cells or a onedimensional CNN with bidirectional coupling
SeckTuohMora: Phenomenology of reactiondiffusion binarystate cellular automata
 Int. J. Bifurcation and Chaos
, 2006
"... We study a binarycellstates eightcell neighborhood twodimensional cellular automaton model of a quasichemical system with a substrate and a reagent. Reactions are represented by semitotalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in st ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
We study a binarycellstates eightcell neighborhood twodimensional cellular automaton model of a quasichemical system with a substrate and a reagent. Reactions are represented by semitotalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if sum of neighbors in state 1 belong to another specified interval. We investigate spacetime dynamics of 1296 automata, establish morphologybases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still life compact patterns). We explore reactiondiffusion like patterns produced in result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.
Sync in Complex Dynamical Networks: Stability, Evolution, Control, and Application
, 2008
"... In the past few years, the discoveries of smallworld and scalefree properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the collective dynamics of complex networks. This paper reports rece ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In the past few years, the discoveries of smallworld and scalefree properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the collective dynamics of complex networks. This paper reports recent progresses in the literature of synchronization of complex dynamical networks including stability criteria, network synchronizability and uniform synchronous criticality in different topologies, and the connection between control and synchronization of complex networks as well. The economiccycle synchronous phenomenon in the World Trade Web, a scalefree type of social economic networks, is used to illustrate an application of the network synchronization mechanism.
Complex Networks: Topology, Dynamics and Synchronization
, 2006
"... This report is a recompilation of the research done during my visit to FernUniversität in Hagen from April 2005 to April 2006. It consists of a tutorial review of the background of Complex Dynamical Networks and some ideas set forward during this research period. The intension is for this manuscript ..."
Abstract
 Add to MetaCart
This report is a recompilation of the research done during my visit to FernUniversität in Hagen from April 2005 to April 2006. It consists of a tutorial review of the background of Complex Dynamical Networks and some ideas set forward during this research period. The intension is for this manuscript to serve as a complement to the report for the DAAD Research Grant that I received to visit Germany and at the same time as a documental reference and background for future work. 1 Financially Supported by DAADResearch Scholarship 2005
Feature Complex Networks: SmallWorld, ScaleFree and Beyond
"... In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and ..."
Abstract
 Add to MetaCart
In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and active field of research. The present article reviews some basic concepts, important progress, and significant results in the current studies of various complex networks, with emphasis on the relationship between the topology and the dynamics of such complex networks. Some fundamental properties and typical complex network models are described; and, as an example, epidemic dynamics are analyzed and discussed in some detail. Finally, the important issue of robustness versus fragility of dynamical synchronization in complex networks is introduced and discussed. Index terms—complex network, smallworld network, scalefree network, synchronization, robustness
c ○ World Scientific Publishing Company CHUA’S PERIODIC TABLE
, 2001
"... An interdisciplinary analysis is presented in this paper on the relationship between the bifurcation behavior of chaotic systems, specifically Chua’s circuit, and the quantized energy level of atoms. We show that it is possible to associate special capacitance values in Chua’s circuits with the elec ..."
Abstract
 Add to MetaCart
An interdisciplinary analysis is presented in this paper on the relationship between the bifurcation behavior of chaotic systems, specifically Chua’s circuit, and the quantized energy level of atoms. We show that it is possible to associate special capacitance values in Chua’s circuits with the electronic energy levels En of atoms calculated from Bohr’s Law. In particular, these particular capacitance values correspond to the bifurcation points αn of Chua’s circuits. We found a functional relation associating a specific Chua’s circuit to the Hydrogen atom and obtained a map of “Atom ” to “Chua’s Circuit”. This map can be extended to other elements in the Periodic Table, thereby demonstrating an almost universal relation between the two different physical systems. With this map we can calculate the energy levels of different atoms from bifurcation diagrams (or viceversa) and express the analytical relations in terms of the two variables αn and En