bluuebunny/crossref_metadata_2025 huggingface dataset:
Emergent volatility in asset markets with heterogeneous agents
Authors: Li Honggang , Rosser J. Barkley
Published: January 2006

This paper examines the emergence of complex volatility in dynamic asset markets when there are heterogeneous agents. A discrete formulation is studied with two categories of market participants, fundamentalist traders who buy when the asset price is below the fundamental value and sell when it is above and noise traders who use moving average technical trading rules that can lead them to chase trends. Agents switch from one type of strategy to the other according to relative returns. A variety of outcomes are studied using numerical simulation, including variation of market price responsiveness to changes in excess demand, in switching behavior, and the introduction of noise. Bifurcation analysis of certain parameters is presented.
Individual‐based lattice model for spatial spread of epidemics
Authors: Fukś Henryk , Lawniczak Anna T.
Published: January 2006

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible‐infected‐removed) type. The automaton is fully discrete, i.e., space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean‐field type description of the automaton, and discuss differences between the mean‐field dynamics and the results ofLGCA simulation.
Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map
Authors: Chen J. Y. , Wong K. W. , Zheng H. Y. , Shuai J. W.
Published: January 2006

An approach to synchronize spatiotemporal chaos is proposed. It is achieved by introducing a finite flat region in the local map. By using this scheme, a number of orbits in both the drive and the response subsystems are forced to pass through a fixed point in every dimension. With only an arbitrary phase space variable as drive signal, synchronization of spatiotemporal chaos can be achieved rapidly in the response subsystem. This is an advantage when compared with other synchronization methods that require a linear combination of the original phase space variables.
On “open‐economy macroeconomics using models of closed systems”
Authors: Correa Romar , Damle Shubhada
Published: January 2006

International macroeconomic crises occur because of the enlargement of the dimension of the state space within which economies operate. Our focus is the recent financial turbulence worldwide in which (i) banks had a role to play and (ii) whole systems collapsed. We validate these propositions in the context of the qualitative theory of differential equations. The economic framework used is that of Wynne Godley.
Short communication: Quantitative spatial analysis of randomly situated surface water bodies through f‐α spectra
Authors: Sagar B. S. Daya
Published: January 2006

A notable similarity is observed between the probability distributions obtained from a data set that contains a large number of randomly situated surface water bodies and the probability distributions estimated by binomial multiplicative process. From these well conformed probability distributions, the generalised information dimensions have been computed through f‐α spectra to characterise and quantify the spatial organisation of
the surface water bodies. It is noticed from the investigated case study that the results
tend to vary by changing the direction of bisecting process. The experimental results on
spatial distribution of surface water bodies of the study area qualify that the computed
generalised information dimensions for the vertical bisecting is rather uniform than that
of the horizontal bisecting process.
Letter to the editor: Generation of self organized critical connectivity network map (SOCCNM) of randomly situated water bodies during flooding process
Authors: Sagar B. S. Daya
Published: January 2006

This letter presents a brief framework based on nonlinear morphological transformations to generate a self organized critical connectivity network map (SOCCNM) in 2‐dimensional space. This simple and elegant framework is implemented on a section that contains a few simulated water bodies to generate SOCCNM. This is based on a postulate that the randomly situated surface water bodies of various sizes and shapes self organize during flooding process.
The resonance phenomenon in the reaction–diffusion systems
Authors: Lebanov A. I. , Chernyaev A. P. , Starozhilova T. K.
Published: January 2006

A new mechanism of pattern formation different from the Turing and oscillatory instabilities in the reaction–diffusion systems was found. It is closely connected with the resonance phenomenon that appears in the models when Jacobi′s matrix of the kinetic part is equivalent to Jordan cell and diffusion coefficients are cited. Some results of numerical calculations of the blood coagulation model are discussed. The pattern formation regimes that can be treated as the results from the resonance phenomenon were observed.
Dynamic processes during accretion into a black hole
Authors: Bisonvatyi-kogan G. S.
Published: January 2006

Accretion disc theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was emitted to the sides of the disc. One of the most important new invention of this theory was a phenomenological treatment of the turbulent viscosity, known as “alpha” prescription, when the (rϕ) component of the stress tensor was approximated by (αP) with a unknown constant α This prescription played the role in the accretion disc theory as well important as the mixing‐length theory of convection for stellar evolution. Sources of turbulence in the accretion disc are discussed, including nonlinear hydrodynamic turbulence, convection and magnetic filed role. In parallel to the optically thick geometrically thin accretion disc models, a new branch of the optically thin accretion disc models was discovered, with a larger thickness for the same total luminosity. The choice between these solutions should be done of the base of stability analysis. The ideas underlying the necessity to include advection into the accretion disc theory are presented and first models with advection are reviewed. The present status of the solution for a low‐luminous optically thin accretion disc model with advection is discussed and the limits for an advection dominated accretion flows (ADAF) imposed by the presence of magnetic field are analyzed.
Biomolecular nonlinear dynamic mechanisms as a foundation for human traits of information processing machine
Authors: Rambaidi Nicholas G.
Published: January 2006

A pseudo‐biological paradigm in information processing launched by McCulloch and Pitts in the early 1940s has been advanced during the last decades. Different attempts were made based on these developments to design operational information processing devices capable of solving problems of high computational complexity.

One of them was the use of nonlinear dynamic mechanisms inherent in information processing by biochemical, biomolecular, and simple biological entities. Chemical reaction–diffusion media proved to be effective tools for the implementation of these capabilities.

Basic features of these information processing means and modeling of their information
processing capabilities are discussed in this paper. Belousov–Zhabotinsky type reaction–diffusion media were used to simulate image processing operations and finding paths in a labyrinth.
Accelerated non‐linear destruction of the earth′s crust
Authors: Artyushkov E. V.
Published: January 2006

The upper part of the Earth—the lithospheric layer, ∼100 km thick, is rigid. Segments of this spherical shell–lithospheric plates are drifting over a ductile asthenosphere. On the continents, the lithosphere includes the Earth′s crust, ∼40 km thick, which is underlain by peridotitic rocks of the mantle. In most areas, at depths ∼20–40 km the continental crust is composed of basalts with density ∼2900kg m−3. At temperature and pressure typical for this depth, basalts are metastable and should transform into another assemblage of minerals which
corresponds to garnet granulites and eclogites with higher densities 3300–3600 kg m−3. The rate of this transformation is extremely low in dry rocks, and the associated contraction of basalts evolves during the time ≥108 a. To restore the Archimede′s equilibrium, the crust subsides with a formation of sedimentary basins, up to 10–15 km deep.

Volumes of hot mantle with a water‐containing fluid emerge sometimes from a deep mantle to the base of the lithosphere. Fluids infiltrate into the crust through the mantle part of the lithosphere. They catalyze the reaction in the lower crust which results in rock contraction with a formation of deep water basins at the surface during ∼106 a. The major hydrocarbon
basins of the world were formed in this way. Infiltration of fluids strongly reduces the viscosity of the lithosphere, which is evidenced by narrow‐wavelength deformations of this layer. At times of softening of the mantle part of the lithosphere, it becomes convectively replaced by a
hotter and lighter asthenosphere. This process has resulted in the formation of many mountain ranges and high plateaus during the last several millions of years. Softening of the whole lithospheric layer which is rigid under normal conditions allows its strong compressive and
tensile deformations. At the epochs of compression, a large portion of dense eclogites that were formed from basalts in the lower crust sink deeply into the mantle. In some cases they carry down lighter blocks of granites and sedimentary rocks of the upper crust which delaminate from eclogitic blocks and emerge back to the crust. Such blocks of upper crustal rocks include diamonds and other minerals which were formed at a depth of 100–150 km.
Technological changes on the macroeconomic level—mathematical modeling
Authors: Shananin A. A.
Published: January 2006

We consider two of the technological changes on the macroeconomic level. The first type is due to changes of addresses of mutual deliveries between producers and the second type is due to technological progress.
Mathematical modeling of an industrial firm in transient economy
Authors: Pospelov I. G.
Published: January 2006

A behavior model of an industrial firm with a possibility of merchandising and purchasing of production on two channels, traditional and commercial, is given. The former is stable, but less profitable due to non‐payments. The latter is profitable, but risky. The model describes different modes of firm operation depending on economic parameters. In such a model, firms have incentives to integrate in financial and industrial groups.
Dissipative nonlinear structures in tokamak plasmas
Authors: Razumova K. A.
Published: January 2006

A lot of different kinds of instabilities may be developed in high temperature plasma located in a strong toroidal magnetic field (tokamak plasma). Nonlinear effects in the instability development result in plasma self‐organization. Such plasma has a geometrically complicated configuration, consisting of the magnetic surfaces imbedded into each other and split into islands with various characteristic numbers of helical twisting. The self‐consistency of the processes means that the transport coefficients in plasma do not depend just on the local parameters, being a function of the whole plasma configuration and of the forces affecting it. By disrupting the bonds between separate magnetic surfaces filled with islands, one can produce zones of reduced transport in the plasma, i.e. “internal thermal barriers”, allowing one essentially to increase the plasma temperature and density.
Stimulus, expectations, desires and response strategies:The building blocks of nonlinear interaction dynamics
Authors: Dendrinos Dimitrios S.
Published: January 2006

Stimulus and response functions, as the fundamental blocks of nonlinear interaction dynamics, are analyzed and modeled here, under a variety of interaction strategies. The backbone of the suggested model is a simple iterative dynamical formulation: the magnitude of a signal sent at present is a function of a relevant signal sent—as well as of a signal received—in the past; in turn, a signal received at present is a function of a signal received—as well as of a signal sent—in the past; namely,

where Ss/r is the size of a signal sent/received, and n
is a point in time.

Expectations and desires by senders and receivers of signals are introduced in the analysis. As a result, a basic classification of individuals emerges, that of “dreamers” and “cynics.” Three fundamental response strategies are identified, all plays on a theoretically Newtonian action–reaction system. A pair of individual, as well as community, interaction end‐states are the focus of the analysis here; their stability properties, under a tit‐for‐tat response strategy, are studied and their likelihood to occur is considered.
In‐phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps
Authors: Astakhov Vladimir , Shabunin Alexey , Klimshin Alexander , Anishchenko Vadim
Published: January 2006

We consider in‐phase and antiphase synchronization of chaos in a system of coupled cubic maps. Regions of stability and robustness of the regime of in‐phase complete synchronization was found. It was demonstrated that the loss of the synchronization is accompanied by bubbling and riddling phenomena. The mechanisms of these phenomena are connected with bifurcations of the main family of periodic orbits and orbits appeared from them. We found that in spite of the in‐phase synchronization, the antiphase self‐synchronization of chaos is impossible for discrete maps with symmetric diffusive coupling. For achieving antiphase synchronization we used method of controlled synchronization by addition feedback. The region of the controlled antiphase synchronization and phenomena which accompany the loss of the synchronization are presented.
Markov chain analysis of weekly rainfall data in determining drought‐proneness
Authors: Banik Pabitra , Mandal Abhyudy , Rahman M. Sayedur
Published: January 2006

Markov chain models have been used to evaluate probabilities of getting a sequence of wet and dry weeks during South‐West monsoon period over the districts Purulia in West Bengal and Giridih in Bihar state and dry farming tract in the state of Maharashtra of India. An index based on the parameters of this model has been suggested to indicate the extend of drought‐proneness of a region. This study will be useful to agricultural planners and irrigation engineers to identifying the areas where agricultural development should be focused as a long term drought mitigation strategy. Also this study will contribute toward a better understanding of the climatology of drought in a major drought‐prone region of the world.
A theoretical analysis of season length restrictions in fisheries management
Authors: Xu Qing , Batabyal Amitrajeet A.
Published: January 2006

This paper studies season length restrictions in fisheries management from an ecological‐economic perspective. We first construct a model of a stylized fishery in which season length restrictions are used to manage the fishery. We then show how the dynamic and the stochastic properties of this fishery can be used to construct two managerial criteria that are meaningful from an ecological standpoint. Finally, using these two criteria, we discuss a probabilistic approach to fisheries management in which the principal focus of a manager is on moving the fishery away from the least desirable state of existence.
Intergenerational equity and dynamic duality principles
Authors: Uzawa Hirofumi
Published: January 2006

The concept of intergenerational equity concerning intertemporal paths of consumption and capital accumulation is introduced and the analysis of the dynamic processes of capital accumulation and changes in environmental quality that are intergenerationally equitable is developed. The analysis is based upon the dynamic duality principles, as originally developed by Koopmans and Uzawa, and later extended to the case involving environmental quality.

A time‐path of consumption and capital accumulation is defined intergenerationally equitable when it is dynamically efficient and, at the same time, the imputed price of each kind of capital, either private capital, or social overhead capital, is identical over time. The existence of an intergenerationally equitable time‐path of consumption and capital accumulation is guaranteed when the processes of various kind of capital are subject to the Penrose effect, exhibiting the law of diminishing marginal rates of investment capital accumulation.
Growth, technology, and environmental change—nonlinearity and non‐constant returns
Authors: Zhang Wei-Bin
Published: January 2006

This paper proposes a growth model with endogenous technology and environmental change. The economy consists of two sectors, production and environmental. The production sector produces goods with knowledge, labor, and capital as inputs under perfect competitive conditions. Knowledge accumulates through learning by doing. The environment is affected by production, consumption, the environmental sector′s production efficiency, and the nature′s purification. The simple model shows that it is difficult to explicitly judge the impact of factors such as environmental policy, knowledge accumulation efficiency and preference change on the environment.
New feedback functions for synchronizing chaotic maps
Authors: Ali M. K.
Published: January 2006

Synchronization of chaotic maps is studied using the method of variable feedback. A general method is presented for generating feedback functions for maps. These feedback functions are found very efficient. Our study shows that when the driver and the response systems are fed by common noise, the noise does not affect synchronization. With different but weak noise added to the driver and response systems, approximate synchronization persists.
Dynamic system evolution and markov chain approximation
Authors: Melnik Roderick V. Nicholas
Published: January 2006

In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs
Authors: Koumboulis F. N. , Skarpetis M. G. , Mertzios B. G.
Published: January 2006

The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous‐domain physical system by means of a discrete multidimensional passive (MD‐passive) dynamic system, using principles of MD nonlinear digital filtering. The resulting integration algorithm is highly robust, thus attenuating the numerical noise during the execution of the steps of the discrete algorithm. The nonlinear discrete equations approximating the inviscid fluid dynamic phenomena are explicitly determined. Furthermore, the WDF circuit realization of the Euler equations is determined. Finally, two alternative MD WDF set of nonlinear equations, integrating the Euler equations are analytically determined.
Irregular Attractors
Authors: Anishchenko Vadim S. , Strelkova Galina I.
Published: January 2006

In this paper the definition of attractor of a dissipative dynamical system is introduced. The classification of the existing types of attractors and the analysis of their characteristics are presented. The discussed problems are illustrated by the results of numerical simulations using a number of real examples that provides the possibility to understand easily the main properties, similarities and differences of the considered types of attractors.
Morphometric relations of fractal‐skeletal based channel network model
Authors: Sagar B. S. Daya , Omoregie Charles , Rao B. S. Prakasa
Published: January 2006

A fractal‐skeletal based channel network (F‐SCN) model is proposed. Four regular sided initiator‐basins are transformed as second order fractal basins by following a specific generating mechanism with non‐random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F‐SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method) are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.
Some remarks on second order linear difference equations
Authors: Zhang B. G. , Tian Chuan Jun
Published: January 2006

We obtain some further results for comparison theorems and oscillation criteria of second order linear difference equations.
Nonlinear dynamics of the additive‐pulse modelocked laser
Authors: Mozdy E. J. , Pollock C. R.
Published: January 2006

We have modeled the additive‐pulse modelocked (APM) laser with a set of four nonlinear difference equations, that describe the transit of optical pulses through the main cavity and through an external cavity containing a single‐mode optical fiber. Simulating the system under several parameter variations, including fiber length, gain, and fiber coupling, we have observed period‐doubling bifurcations into chaos. In addition, the model predicted large regimes of quasiperiodicity, and crisis transitions between different chaotic regions. We have used the method of nearest neighbors, Lyapunov exponents, and attractor reconstruction to characterize the chaotic regimes and the different types of bifurcations. We have included bandwidth‐limiting and monitoring provisions to prevent non‐physical solutions. To our knowledge, this is the first such characterization of chaos in the APM laser, as well as the first evidence of crisis behavior.
Cities and cellular automata
Authors: White Roger
Published: January 2006

Cellular automata provide a high‐resolution representation of urban spatial dynamics.Consequently they give the most realistic predictions of urban structural evolution, and in particular they are able to replicate the various fractal dimensionalities of actual cities. However, since these models do not readily incorporate certain phenomena like density measures and long‐distance (as opposed to neighbourhood) spatial interactions, their performance may be enhanced by integrating them with other types of urban models.Cellular automata based models promise deeper theoretical insights into the nature of cities as self‐organizing structures.
Coupled flare attractors – a discrete prototype for economic modelling
Authors: Hartmann Georg C. , Rossler Otto E.
Published: January 2006

A chaotic environment can give rise to “flares” if an autocatalytic variable responds in a multiplicative, threshold–type fashion to the environmental forcing. An “economic unit” similarly depends in its growth behavior on the unpredictable (chaotic?) buying habits of its customers, say. It turns out that coupled flare attractors are surprisingly robust in the sense that the resulting “economy” is largely independent of the extent of diffusive coupling used.Some simulations are presented.
Thermal noise and the incessant vibration of the outer hair cells in the cochlea
Authors: Fritze W. , Steurer M.
Published: January 2006

The continual exposure of outer hair cells (OHCs) to thermal noise causes vibrations in resonant frequency. As these vibrations are backprojected, they should be recordable as audiofrequencies in the outer ear canal. But even though they are likely to be amplified in some areas by clustering in terms of the chaos theory, they cannot be picked up in the outer ear canal by currently available recording technologies. Conditions change in the presence of pathology, e.g. loss of OHCs and fibrous replacement: Clusters grow in size and amplitudes become larger so that the vibrations can be picked up as spontaneous oto‐acoustic emissions (SOAEs) in the outer ear canal. Efforts are needed to demonstrate the presence of physiological OHC vibrations (emission by incessant vibration, EIV) by processing auditory recordings with statistical methods.
Dynamic ensembles with variable structure and friction simulation
Authors: Feldstein I. V. , Kuzmin N. N.
Published: January 2006

The paper presents an approach to the simulation of friction interaction. The model does not use any physical descriptions of the processes in the system, but it has simple physical interpretation. It is based on one qualitative experimental result – the value of first Lyapunov exponent drops with normal load. It is shown that the logistic map could be considered as the simplest model of continuous contact. The generalization of the model (which takes into account the discreteness of the real contact) gives results very similar to the experimental ones. It is in the form of a dynamic ensemble with variable structure (DEVS), which has some interesting properties – particularly bifurcation diagrams.
Simulation of land use evolution by discrete events method: Application to “la chaîne des puys” from XV to XVIII Century
Authors: Michelin Y. , Poix C.
Published: January 2006

By using a discrete event method, simulation of land use evolution has been applied to a landscape model of “la ChaÎne des Puys” (French Massif Central) during along period (XV–XVIII centuries). The indications concerning the evolution of land use are in conformity with the observation of actual situations but the dynamic changes are faster than in actual facts. In spite of limitations due to necessary simplifications, it is now established that the discrete event method is efficient to simulate land use evolution during a long period. The model is immediately able to describe actual dynamics and to show sensitive variables with their critical values. Although oversimplified, it shows how far factors such as level of crops production and taxation can influence land use and landscape changes with a more or less lengthy period. In the future, the model should be bettered by introducing other determined and/or stochastic events.
Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point
Authors: Ebelings Werner , Rateitschak Katja
Published: January 2006

This paper aims to make further contributions to the exploration of the symbolic dynamics generated by the logistic map at Feigenbaum accumulation point. In particular we are interested in the grammar of these sequences; completing earlier studies we study here arbitrary partitions also. Our main aim is the investigation of the special grammars which characterize the long‐range correlations between letters. Considering these sequences as standard examples of a complex system, we introduce and discuss a complexity function derived from the conditional entropies. Further we discuss local predictabilities.
The study of bray–liebhafsky reaction over a wide range of temperatures. I. experimental contributions
Authors: Vîlcu R. , Danciu T. , Bala D.
Published: January 2006

Some experiments with a classical Bray–Liebhafsky system over a wide range of (assuming constant) temperatures were performed. The observed behavior shows (at least) one critical point. A qualitative interpretation is proposed.
Statistical polymer method: Modeling of macromolecules and aggregates with branching and crosslinking, formed in random processes
Authors: Romm Freddy A. , Figovsky Oleg L.
Published: January 2006

The statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non‐equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels,associates in polar liquids and other aggregates.
Morphogenesis of an institution on a lattice game
Authors: Agliardi Elettra , Giovannetti Emanuele
Published: January 2006

In this paper we study the morphogenesis of an institution when local social interactions are taken into account. The structure we obtain has characteristics of “self‐organized criticality”. After a transient period the system self‐organizes into a configuration which is compatible with a high degree of differentiation among different sites and generates typical power laws.
How and why do neurons generate complex rhythms with various frequencies?
Authors: Chay Teresa Ree , Lee Young Seek
Published: January 2006

Some neurons generate endogenous rhythms with a period of a few hundred milliseconds,while others generate rhythms with a period of a few tens of seconds. Sometimes rhythms appear chaotic. Explaining how these neurons can generate various modes of oscillation with a widely ranging frequency is a challenge. In the first part of this review, we illustrate that such rhythms can be generated from simple yet elegant mathematical models. Chaos embedded in rhythmic activity has interesting characteristics that are not seen in other physical systems. Understanding of how these neurons utilizes endogenous rhythms to communicate with each other is important in elucidating where the brain gets various rhythms and why it can pervert into abnormal rhythms under diseased conditions. Using the islet of Langerhans in pancreas as an example, in the second part of this review, we illustrate how insulin secreting β‐cells communicate with glucagon secreting α‐cells to achieve an optimal insulin release.
Pattern recognition using chaotic neural networks
Authors: Tan Z. , Hepburn B. S. , Tucker C. , Ali M. K.
Published: January 2006

Pattern recognition by chaotic neural networks is studied using a hyperchaotic neural network as model. Virtual basins of attraction are introduced around unstable periodic orbits which are then used as patterns. Search for periodic orbits in dynamical systems is treated as a process of pattern recognition. The role of synapses on patterns in chaotic networks is discussed. It is shown that distorted states having only limited information of the patterns are successfully recognized.
Chaotic attractors of two‐dimensional invertible maps
Authors: Anishchenko Vadim S. , Vadivasova Tatjana E. , Strelova Galina I. , Kopeikin Andrey S.
Published: January 2006

In this paper, we investigate the characteristics of quasihyperbolic attractors and quasiattractors in Invertible dissipative maps of the plane. The criteria which allow one to diagnose the indicated types of attractors in numerical experiments are formulated.
Oscillation of certain partial difference equations
Authors: Choi Sung Kyu , Zhang Bing Gen
Published: January 2006

We first obtain sufficiency conditions for the oscillation of all solutions of linear partial difference equation

urn:x-wiley:10260226:media:ddns723596:ddns723596-math-0001

. Next, we establish a linearized oscillation result for the nonlinear partial difference equation

urn:x-wiley:10260226:media:ddns723596:ddns723596-math-0002

.
Simulation of earthquakes with cellular automata
Authors: Akishin P. G. , Altaisky M. V. , Antoniou I. , Budnik A. D. , Ivanov V. V.
Published: January 2006

The relation between cellular automata (CA) models of earthquakes and the Burridge–Knopoff (BK) model is studied. It is shown that the CA proposed by P. Bak and C. Tang,although they have rather realistic power spectra, do not correspond to the BK model. We present a modification of the CA which establishes the correspondence with the BK model.An analytical method of studying the evolution of the BK‐like CA is proposed. By this method a functional quadratic in stress release, which can be regarded as an analog of the event energy, is constructed. The distribution of seismic events with respect to this “energy” shows rather realistic behavior, even in two dimensions. Special attention is paid to two‐dimensional automata; the physical restrictions on compression and shear stiffnesses are imposed.
Numerical simulations through first order nonlinear difference equation to study highly ductile symmetric fold (HDSF) dynamics: A conceptual study
Authors: Sagar B. S.
Published: January 2006

Changes in morphology of a geological fold are due to stress and internally exerting forces (IEFs). Such morphological changes can be quantified in terms of fractal dimensions. Stress and the fractal dimension are depicted in normalized scale as dimensionless parameters.Incorporating these parameters in a first order nonlinear difference equation that has physical relevance as the simplest viable model of a symmetric fold sustaining morphological changes,numerical simulations are carried out which are analogous to creep experiments. In the first experiment, the constant stress (λ) is employed to model the morphological dynamical behaviour of highly ductile symmetric folds (HDSFs) that are postulated as they are precarious to stress and IEF, and will not supervene the state of brittleness during the evolution. In the second experiment, the time dependent stress that is changed according to a dynamical rule is used to model distinct dynamical behaviors of these HDSFs.The results arrived through computer simulations are the attractor interlimb angles (AIAs).Bifurcation diagrams are also depicted to show the dynamical behaviors concerning the change in the stress dynamics.
Towards a theory of mind
Authors: Boyarsky Abraham
Published: January 2006

The language of nonlinear dynamical systems and ergodic theory is used to present a theoretical framework for the study of mind. The basic space X
consists of the collection of all brain images (clusters of activated neurons) that are relevant to consciousness. The dynamics of the brain is modelled by means of a discrete time transformation T
which takes a cluster of activated brain cells into another cluster of activated brain cells. The space X
is partitioned into subcollections of brain images, namely those generated by the five senses and by other processes that produce brain images relevant to consciousness. It is argued that T is a Markov transformation with respect to this partition of X. This leads to the existence of an object μ, referred to as an SRB measure which possesses properties that make it a candidate for mind: μ is ‘aware’ of the brain images in its support; μ is time‐invariant and acts as an attractor into which all orbits of (conscious) brain images settle. Furthermore, the dynamical systems model for mind allows the estimation of brain information rates and provides a framework in which a number of mind related issues can be discussed.
Blowout bifurcation of chaotic saddles
Authors: Kapitaniak Tomasz , Lai Ying-Cheng , Grebogi Celso
Published: January 2006

Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.
Emergence of collective behavior in a system of autonomous agents
Authors: Antoniou I. , Bosco F. , Ivanov V. V. , Kisel I. V.
Published: January 2006

We study the properties of emergent collective behavior in a system of interacting autonomous agents. The system evolves in time according to two rules of communication, one from interactions between agents and another one from interactions of the agents with an additional agent which evolves in time in a periodic and stable manner. The application of these two rules is decided by a prescribed probability distribution. We analyze the emergence and the efficiency (coordination) with which collective patterns are constructed in time as a function of the parameters of the system.
Coupled flare attractors – a discrete prototype for economic modelling
Authors: Hartmann Georg C. , Rossler Otto E.
Published: January 2006

A chaotic environment can give rise to “flares” if an autocatalytic variable responds in a multiplicative, threshold‐type fashion to the environmental forcing. An “economic unit” similarly depends in its growth behavior on the unpredictable (chaotic?) buying habits of its customers, say. It turns out that coupled flare attractors are surprisingly robust in the sense that the resulting “economy” is largely independent of the extent of diffusive coupling used. Some simulations are presented.
Anomalous resistance of the fractal current‐carrying corona of Z‐pinch
Authors: Kingsep A.
Published: January 2006

An effect of the random plasma inhomogeneity onto the scenario of ion‐acoustic anomalous resistivity is considered. It is shown that such an inhomogeneity could be more efficient than nonlinear effects to determine the turbulent resistivity. In application to Z‐pinches, some peculiarities of the skin‐effect are considered, in particular, subsequent inhomogeneity of the current penetration into the conducting medium.
Cognition: Differential‐geometrical view on neural networks
Authors: Buffalov S. A.
Published: January 2006

A neural network taken as a model of a trainable system appears to be nothing but a dynamical system evolving on a tangent bundle with changeable metrics. In other words to learn means to change metrics of a definite manifold.
A note on the global attractivity of a discrete model of nicholson′s blowflies
Authors: Zhang B. G. , Xu H. X.
Published: January 2006

In this paper, we further study the global attractivity of the positive equilibrium of the discrete Nicholson′s blowflies model

urn:x-wiley:10260226:media:ddns362607:ddns362607-math-0001

. We obtain a new criterion for the positive equilibrium N∗
to be a global attractor, which improve the corresponding results obtained by So and Yu (J. Math. Anal. Appl. 193 (1995), 233–244).
Stability of a time discrete perturbed dynamical system with delay
Authors: Gil′ Michael I. , Cheng Sui Sun
Published: January 2006

Let Cn be the set of n complex vectors endowed with a norm . Let A, B be two complex n × n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type

urn:x-wiley:10260226:media:ddns317646:ddns317646-math-0002

, where Fk : Cn × Cn → Cn satisfies the condition

urn:x-wiley:10260226:media:ddns317646:ddns317646-math-0003

, where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.
Metaphors and social science
Authors: Macpherson Eric D.
Published: January 2006

The social sciences have a considerable history of attempts to apply models and theories from the physical sciences. All such attempts have failed, primarily because social scientists have commonly not distinguished between applications and possibly useful metaphors.

Attempts to apply non‐linear mathematics to social concerns will similarly fail. There are now no non‐trivial applications, and there are unlikely ever to be.

But the phenomenon of reifying models and theories from elsewhere has long standing status in the social sciences, and DDNS can play an important role in monitoring those attempts.
Population growth and environment as a self‐organizing system
Authors: Allen Peter M.
Published: January 2006

Over recent years a new understanding of complex systems, and their dynamics and evolution has emerged, and these have been shown to provide a new basis for models of the changing patterns of population and economic activities that shape the landscape. In this paper we
make clear the necessarily partial description that any particular model must provide, and show the importance of a multidisciplinary, holistic understanding, linking any particular model to the co‐evolution of its environment. In addition, we show how evolutionary processes link the microscopic level of molecules through successive scales of structure and organization ultimately to the biosphere itself, to issues of climatic change, of biomes at the continental scale and atmospheric and oceanic circulation patterns. Some very recent results will be shown which demonstrate that the world climate has already been modified
considerably by human activities, particularly agriculture, underlining the vital need to understand better the on‐going interaction between human activities and the biosphere.

Models will be described which can link the co‐evolution of these multiple scales of organization and change, and which can be used to help to explore the consequences of different possible policies, and in this way to provide information concerning the agendas, risks and issues to be addressed in the 21st Century, as well as pointing to possible policies
that may be appropriate. Already models exist which can explore the dynamics of urban development, the patterns of land‐use, and the possible environmental impacts of these in the context of a still fast growing population. Such models provide a framework within which questions such as those concerning energy consumption, transportation, social conditions can be explored and agendas and priorities set. Clearly, advances in information and telecommunications technologies present great opportunities for increasing accessibilities without necessarily increasing mobility or energy consumption, and models which can
help in assessing their potential impact on development and in their successful implementation are of great value.

Complex system models can also be of great use in exploring the long term implications of the present, increasing, reliance on market systems and economic signals in the allocation of resources and patterns of investment. In particular, complex systems models can explore the effects of the precise regulatory framework within which a market operates, and as a result may be able to suggest ways in which long term, sustainable development can be achieved despite the present short term horizons of the players in market dynamics. In addition, of course, they can illuminate and inform actors about the longer term, and perhaps actually lengthen the time horizon considered by market participants. In short, the insights arising from complex systems models could, hopefully, play a role in expanding the understanding, the conceptual framework and the ethical basis of decision making in the 21st Century.
Self‐organized criticality and urban development
Authors: Batty Michael , Xie Yichun
Published: January 2006

Urban society is undergoing as profound a spatial transformation as that associated with the emergence of the industrial city two centuries ago. To describe and measure this transition, we introduce a new theory based on the concept that large‐scale, complex systems composed
of many interacting elements, show a surprising degree of resilience to change, holding themselves at critical levels for long periods until conditions emerge which move the system, often abruptly, to a new threshold. This theory is called ‘self‐organized criticality’; it is consistent with systems in which global patterns emerge from local action which is the hallmark of self‐organization, and it is consistent with developments in system dynamics and their morphology which find expression in fractal geometry and weak chaos theory. We illustrate the theory using a unique space–time series of urban development for Buffalo,
Western New York, which contains the locations of over one quarter of a million sites coded by their year of construction and dating back to 1773, some 60 years before the city began to develop. We measure the emergence and growth of the city using urban density functions from which measures of fractal dimension are used to construct growth paths of the way the city has grown to fill its region. These phase portraits suggest the existence of transitions
between the frontier, the settled agricultural region, the centralized industrial city and the decentralized postindustrial city, and our analysis reveals that Buffalo has maintained itself at a critical threshold since the emergence of the automobile city some 70 years ago. Our implied speculation is: how long will this kind of urban form be maintained in the face of seemingly unstoppable technological change?
Self‐organization in interface dynamics and urban development
Authors: Meron Ehud
Published: January 2006

The view of the urban environment as an extended nonlinear system introduces new concepts, motivates new questions, and suggests new methodologies in the study of urban dynamics. A review of recent results on interface dynamics in nonequilibrium physical systems is presented, and possible implications on the urban environment are discussed. It is suggested that the growth modes of specific urban zones (e.g. residential, commercial, or industrial) and the factors affecting them can be studied using mathematical models that capture two generic interface instabilities.
From fast to slow processes in the evolution of urban and regional settlement structures
Authors: Weidlich Wolfgang
Published: January 2006

Complex systems consist of many intertwined organizational levels starting from micro‐structures and ending with macrostructures. Their evolution takes place on different time scales: Micropatterns exhibit a fast dynamics whereas macropatterns develop slowly. Urban and regional science can make use of this fact by constructing a hierarchy of models on different spatio‐temporal scales.

Based on this understanding two models are presented: One for the relatively fast urban evolution on the microscale and one for the relatively slow regional evolution on the macroscale.

The micromodel considers the urban structure as a system of sites on which different kinds of buildings (dwellings, schools, stores, service‐stations, factories … ) can be erected. The step by step evolution of the city configuration is treated as a stochastic process guided by desirability considerations. The formalization of this concept leads to equations for the evolution of the urban city configuration. Numerical simulations illustrate this urban “microdynamics”.

The macromodel treats the settlement formation in a region on a more global scale. The evolution of the density of economically active populations who produce and consume goods is considered. The driving force of density changes is the spatial difference of incomes motivating the individuals to migrate to locations of optimal income. This nonlinear process leads to the self‐organization of spatially heterogeneous population distributions forming the settlements. Their micro‐structure can thereupon be treated by the micromodel.
Modeling population dynamics in the city: From a regional to a multi‐agent approach
Authors: Benenson Itzhak
Published: January 2006

The paper reviews different approaches to urban population from the point of view of the theory of complex systems. Regional models deal with large numbers of urban regions
involved in exchanging population and resources among themselves. In contrast, ecological models deal with several qualitatively different types of relationships between a small number of components, aimed at understanding the most general laws of urban dynamic. Two relatively new approaches, namely Cellular Automata and multi-agent ones describe the macro‐processes resulting from uniform collective processes at the micro‐level of land parcels and migrating city individuals. Recent results of the multi‐agent simulations regarding abstract and real‐world systems are presented in more details.