bluuebunny/crossref_metadata_2025 huggingface dataset:
“Discrete” Oscillations and multiple attractors in kick‐excited systems
Authors: Damgov V. , Popov I.
Published: January 2006

A class of kick‐excited self‐adaptive dynamical systems is formed and proposed. The class is characterized by nonlinear (inhomogeneous) external periodic excitation (as regards to the coordinates of excited systems) and is remarkable for its objective regularities: the phenomenon of “discrete” (“quantized”) oscillation excitation and strong self‐adaptive stability. The main features of these systems are studied both numerically and analytically on the basis of a general model: a pendulum under inhomogeneous action of a periodic force which is referred to as a kicked pendulum. Multiple bifurcation diagram for the attractor set of the system under consideration is obtained and analyzed. The complex dynamics, evolution and the fractal boundaries of the multiple attractor basins in state space corresponding to energy and phase variables are obtained, traced and discussed. A two‐dimensional discrete map is derived for this case. A general treatment of the class of kick‐excited self‐adaptive dynamical systems is made by putting it in correspondence to a general class of dissipative twist maps and showing that the latter is an immanent tool for general description of its behavior.
Discretizations of a perturbed logistic equation
Authors: Moreles Miguel Angel , Solis francisco
Published: January 2006

The logistic equation has been used to model a population where the intrinsic rate of growth is a linearly decreasing function of the population density. We propose some models arising from discretizations of perturbed logistic equation where external factors such as harvesting
and migration are included. The different discretizations exhibit diverse dynamic asymptotic behavior when dependence on two control parameters are allowed. We also give an alternative method to provide with new models that produce better approximating solutions.
Rationals, periodicity and chaos: A Pythagorean view and a conjecture into socio‐spatial dynamics
Authors: Dendrinos Dimitrios S.
Published: January 2006

Deep in the fascinating world of numbers there still might lurk useful insights into the processes of the socio‐spatial world. A rich section of the world of numbers is of course Number Theory and its pantheon of findings, a part of which is revisited here.

It is suggested in this note that a smooth sequence of seemingly random periodic cycles hides the absence of chaotic dynamics in the sequence. Put differently, a seemingly chaotic sequence of periodic cycles, no matter the bandwidth, implies absence of chaotic motion at any point in the sequence; and conversely, the presence of chaotic motion at any specific point in the sequence implies smooth sequence of periodic cycles at any point in the sequence prior to the onset of quasi periodic or chaotic motions.

To make this conjecture, the paper draws material from the well known property of rational numbers in Number Theory, namely that the division of unity by any integer will always produce a sequence of decimals in some form of periodicity. The conjecture is taken in a liberally interpreted “Pythagorean type” context, whereby a general principle is suggested to be present in all natural or social systems dynamics. Thus, the paper′s subtitle.
The thermodynamic natural path in chemical reaction kinetics
Authors: garfinkle Moishe
Published: January 2006

The Natural Path approach to chemical reaction kinetics was developed to bridge the considerable gap between the Mass Action mechanistic approach and the non‐mechanistic irreversible thermodynamic approach. The Natural Path approach can correlate empirical kinetic data with a high degree precision, as least equal to that achievable by the Mass‐Action rate equations, but without recourse mechanistic considerations. The reaction velocities
arising from the particular rate equation chosen by kineticists to best represent the kinetic behavior of a chemical reaction are the natural outcome of the Natural Path approach. Moreover, by virtue of its thermodynamic roots, equilibrium thermodynamic functions can be extracted from reaction kinetic data with considerable accuracy. These results support the intrinsic validity of the Natural Path approach.
Discrete versus continual description of solid state reaction dynamics from theangle of meaningful simulation
Authors: Korobov A.
Published: January 2006

Chemical dynamics provides quite a number of examples of interesting and useful discrete models. But it catches one′s eye that the majority of them are from the field of homogeneous chemistry. Whereas the chemical individuality of solid substances is represented in discrete terms of crystal lattices, the conventional description of solid state reaction dynamics is
essentially continual. The recent progress in the theory of random mosaics and theory of planigons opens the way for developing an alternative discrete description in terms of Dirichlet tessellations. In the present paper the two approaches are compared from the angle of meaningful simulation. It seems that this may be of interest not only for chemists but also in the broad context of developing and employing discrete dynamical models.
Quasi‐discreted dynamics of a neural net: The lighthouse model
Authors: Haken Hermann
Published: January 2006

This paper studies the features of a net of pulse‐coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ‐functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ‐functions, the phase‐equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. We admit a general dependence of input and coupling strengths on the
neuronal indices. In detail, the results are

(1) exact solution of the phase‐locked state;

(2) stability of phase‐locked state with respect to perturbations, such as phase jumps and
random fluctuations, the correlation functions of the phases are calculated;

(3) phase shifts due to spontaneous opening of vesicles or due to failure of opening;

(4) effect of different sensory inputs on axonal pulse frequencies of coupled neurons.
Synchronization of cardiorhythm by weak external forcing
Authors: Anishchenko V. S. , Balanov A. G. , Janson N. B. , Igosheva N. B. , Bordyugov G. V.
Published: January 2006

We study the possibility to synchronize cardiorhythm of a human by periodic and aperiodic sequences of light and sound pulses. Aperiodic forcing is defined by variation of RR intervals of another subject. Phase locking between cardiorhythm and weak external forcing is detected on finite time intervals. We observe the 1 : 1 synchronization for periodic forcing and n : m
synchronization for aperiodic one.
Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems
Authors: Stefanski Andrzej , kapitaniak Tomasz
Published: January 2006

We describe the method of estimation of the largest Lyapunov exponent of nonsmooth dynamical systems using the properties of chaos synchronization. The method is based on the coupling of two identical dynamical systems and is tested on two examples of Duffing
oscillator: (i) with added dry friction, (ii) with impacts.
Phase fronts and synchronization patterns in forced oscillatory systems
Authors: Meron Ehud
Published: January 2006

This is a review of recent studies of extended oscillatory systems that are subjected to periodic temporal forcing. The periodic forcing breaks the continuous time translation symmetry and leaves a discrete set of stable uniform phase states. The multiplicity of phase states allows for front structures that shift the oscillation phase by π/n where n = 1, 2, …,
hereafter π/n‐fronts. The main concern here is with front instabilities and their implications on pattern formation. Most theoretical studies have focused on the 2 : 1 resonance where the system oscillates at half the driving frequency. All front solutions in this case are π‐fronts. At high forcing strengths only stationary fronts exist. Upon decreasing the forcing strength the stationary fronts lose stability to pairs of counter‐propagating fronts. The coexistence of counter‐propagating fronts allows for traveling domains and spiral waves. In the 4 : 1
resonance stationary π‐fronts coexist with π/2‐fronts. At high forcing strengths the stationary π‐fronts are stable and standing two‐phase waves, consisting of successive oscillatory domains whose phases differ by π, prevail. Upon decreasing the forcing strength the stationary π‐fronts lose stability and decompose into pairs of propagating π/2‐fronts. The instability designates a transition from standing two‐phase waves to traveling four‐phase waves. Analogous decomposition instabilities have been found numerically in higher 2n : 1 resonances. The available theory is used to account for a few experimental observations made on the photosensitive Belousov–Zhabotinsky reaction subjected to periodic illumination.
Observations not accounted for by the theory are pointed out.
Phase multistability of synchronous chaotic oscillations
Authors: Vadivasova T. E. , Sosnovtseva O. V. , Balanov A. G. , Astakhov V. V.
Published: January 2006

The paper describes the sequence of bifurcations leading to multistability of periodic and chaotic synchronous attractors for the coupled Rössler systems which individually demonstrate the Feigenbaum route to chaos. We investigate how a frequency mismatch affects this
phenomenon. The role of a set of coexisting synchronous regimes in the transitions to and between different forms of synchronization is studied.
Invariant manifolds and cluster synchronization in a family of locally coupled map lattices
Authors: belykh Vladimir , Blykh Igor , Komrakov Nikolai , Moseklide Erik
Published: January 2006

This paper presents an analysis of the invariant manifolds for a general family of locally coupled map lattices. These manifolds define the different types of full, partial, and anti‐phase chaotic synchronization that can arise in discrete dynamical systems. Existence of
various invariant manifolds, self‐similarity as well as orderings and embeddings of the manifolds of a coupled map array are established. A general variational equation for the stability analysis of invariant manifolds is derived, and stability conditions for full and partial chaotic synchronization of concrete coupled maps are obtained. The general results are illustrated through examples of three coupled two‐dimensional standard maps with damping.
Nonlinear control of chaotic systems:A switching manifold approach
Authors: Fang Jin-Qing , Hong Yiguang , Qin Huashu , Chen Guanrong
Published: January 2006

In this paper, a switching manifold approach is developed for nonlinear feed‐back control of chaotic systems. The design strategy is straightforward, and the nonlinear control law is the simple bang–bang control. Yet, this control method is very effective; for instance, several
desired equilibria can be stabilized by using one control law with different initial conditions. Its effectiveness is verified by both theoretical analysis and numerical simulations. The Lorenz system simulation is shown for the purpose of illustration.
The dirichlet boundary conditions and related natural boundary conditions in strengthened sobolev spaces for discretized parabolic problems
Authors: D′Yakonov E.
Published: January 2006

Correctness of initial boundary value problems and their discretizations are analyzed under unusual second‐order boundary conditions, which can be considered as natural boundary conditions in strengthened Sobolev spaces and as improvements (in some cases) of the classical Dirichlet boundary conditions. Special attention is paid to optimal perturbation estimates for new variants of the penalty method with respect to the Dirichlet conditions.
The effect of radiation on the stochastic web
Authors: Ashkenazy Y. , Horwitz L. P.
Published: January 2006

A charged particle circling in a uniform magnetic field and kicked by an electric field is considered. An iterative map is developed, under the assumption of small magnetic field. Comparison between the (relativistic) non‐radiative case and the (relativistic) radiative case
shows that in both cases one can observe a stochastic web structure, and that both cases are
qualitatively similar.
A comparative dynamical analysis of Hebrew texts
Authors: Boyarsky Abraham , Góra Pawel
Published: January 2006

Three Hebrew texts, one of them the Hebrew bible, are investigated using dynamical analysis. First, the average mutual information for each of the texts is determined. The first minimum occurs at T = 3 in all three cases, suggesting that 3‐letter words are sufficient to study the dynamical properties of the texts. Using 3‐letter words as the state space for each of the text, we construct a Markov chain model and compute the relative measure–theoretic entropy for each of the texts and use this tool as a means of comparing the information content of the three texts.
Discretized representations of harmonic variables by bilateral Jacobi operators
Authors: Ruffing Andreas
Published: January 2006

Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q‐oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non‐interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.
Chaotic dynamics in a flexible exchange rate system:A study of noise effects
Authors: Asada Toichiro , Misawa Tetsuya , Inaba Toshio
Published: January 2006

In this paper, we investigate by means of analytical method and numerical simulations the properties of three‐dimensional business cycle model, in which foreign exchange rate is flexible and a parameter is fluctuated by noise. The model is a discrete time version of Asada
(Journal of Economics, 62, 239–269,1995)′s continuous time open economy model without noise. We show (1) noise may suppress the burst of flexible foreign exchange rate when its behavior begins to burst as a bifurcation parameter (adjustment speed of the goods market) is increased, (2) the windows of cycles can be broken by noise, and (3) noise may reveal the hidden structures.
A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects
Authors: Asada Toichiro , Inaba Toichio , Misawa Tetsuya
Published: January 2006

In this paper, we formulate a discrete time version of the Kaldorian macrodynamic model in a small open economy with fixed exchange rates. The model is described by a system of the three‐dimensional nonlinear difference equations with and without stochastic disturbances (noise effects). We study the local stability/instability properties analytically by using the linear approximation method, and chaotic dynamics with and without noise effects are investigated by means of numerical simulations. In general, it is believed that the effect of the noise is to obscure the basic structure of the system. But, this is not necessarily the case. We show by means of numerical analysis that the noise can reveal the hidden structure of the model contrary to the usual intuition in some situations.
Critical bifurcation surfaces of 3D discrete dynamics
Authors: Sonis Michael
Published: January 2006

This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n‐dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction) of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
A rainfall simulation model for agricultural development in Bangladesh
Authors: Rahman M. Sayedur
Published: January 2006

A rainfall simulation model based on a first‐order Markov chain has been developed to simulate the annual variation in rainfall amount that is observed in Bangladesh. The model has been tested in the Barind Tract of Bangladesh. Few significant differences were found between the actual and simulated seasonal, annual and average monthly. The distribution of number of success is asymptotic normal distribution. When actual and simulated daily rainfall data were used to drive a crop simulation model, there was no significant difference of rice yield response. The results suggest that the rainfall simulation model perform adequately for many applications.
Difference equation for a population model
Authors: Suzuki Mami
Published: January 2006

In this paper we consider a difference equation of the form

, for t > −∞, seems to be a general statement of a relative socio‐spatial dynamics. Indeed this equation is one of “population model”. We investigate behavior of solutions and expression of analytic general solutions of this model.
Theoretical foundation for jung′s “Mandala Symbolism” based on discrete chaotic dynamics of interacting neurons
Authors: Gontar V.
Published: January 2006

Based on discrete chaotic dynamics algorithms different patterns in a form of mandalas have been generated. This fact gives us the possibility to make a link between mechanism of biochemical reaction dynamics undergoing in brain resulted to the brain creativity process in form of mandalas. Obtained patterns can be related to the space distributed chemicals according to the law of extended principle of maximum entropy, consideration of the information exchange during biochemical transformations, mass conservation law and discrete chaotic dynamics principles.
Controlling hopf bifurcations: Discrete‐time systems
Authors: Chen Guanrong , Fang Jin-quing , Hong Yiguang , Qin Huashu
Published: January 2006

Bifurcation control has attracted increasing attention in recent years. A simple and unified state‐feedback methodology is developed in this paper for Hopf bifurcation control for discrete‐time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
Modeling and analysis of a simple manufacturing‐oriented multi‐agent system
Authors: Levi P. , Schanz M. , Avrutin V.
Published: January 2006

Due to the autonomy of individual agents and the use of the concept of distributed planning, multi‐agent systems (MAS) represent a promising approach to achieve fault‐tolerant self‐organizing manufacturing systems. In this article, a basic component of a manufacturing‐oriented MAS is presented. The negotiation strategies are formulated in such a way that they, on the one hand, guarantee considerable flexibility of the basic component itself, and, on the other hand, enable the construction of more complex systems built up from several components. On the basis of this single component, it is shown that the dynamics of such systems without appropriate control mechanisms can be chaotic. Such behaviour is, however, unwanted in practice and must therefore be stabilized or avoided. In order to develop appropriate tools for this task, the dynamic behaviour of the system is investigated using concepts and methods of synergetics and the theory of nonlinear dynamical systems.
Fractal evolution of a crack network in overburden rock rtratum
Authors: Yu Guangming , Xie Heping , Zhoa Jianfeng , Yang Lun
Published: January 2006

A quantitative description for the spatial distribution and the evolution of a crack network in mining rock stratum is one of the most difficult and fundamental problem in the subject of surface subsidence. In this paper, the physical models are employed to simulate the spatial distribution of a crack network. By using the fractal geometry, the self‐similarity of spatial distribution of crack network is discovered. As a result, the conception of fractal crack network is proposed. Furthermore, the evolution of a crack network with the increasing of mining width is investigated. It is shown that (1) the spatial distribution of a crack network displays the fractal behavior, so, the fractal dimension can be used to describe quantitatively the evolution of the crack network, (2) the fractal dimension of the crack network increases with increasing of mining width, (3) the surface subsidence increases with the increasing of fractal dimension of crack network.
Self‐organization through decoupling
Authors: Correa Romar
Published: January 2006

In one line of research, the transition from Fordism to flexible specialisation is explained by the infeasibility of a mode of regulation that relied on central controls. According to another explanation, which we favour, the disintegration of vertically integrated production is unpredictable. The concept of self‐organization is often recommended to model the transition from hierarchical organizational forms to flatter structures. Formally, a conditionally stable nonlinear system of differential equations is examined. In the first thesis, the characteristic roots with positive real parts play the role of ‘order’ parameters which can become unstable modes. The rest of the variables refer to stable modes. The strategy is to show that the stable modes can be expressed in terms of the unstable modes so that the former can be eliminated from the system. On the other hand, we provide a theorem showing that a coupled set of differential equations can become uncoupled and vice versa as an argument in favour of the second thesis. The path of evolution can turn both ways.
p‐Adic discrete dynamical systems and collective behaviour of information states in cognitive models
Authors: Khrennikov Andrie
Published: January 2006

We develop a model of functioning of complex information systems (in particular, cognitive systems) in that information states are coded by p‐adic integers. An information state evolves by iterations of a discrete p‐adic dynamical system. The p‐adic utrametric on the space of information states (p‐adic homogeneous tree) describes the ability of an information system to operate with associations. The main attention is paid to the collective dynamics of families of associations.
Multi‐fractal‐interslipface angle curves of a morphologically simulated sand dune
Authors: Sagar B. S. Daya
Published: January 2006

A sand dune is simulated by means of a non‐linear mathematical morphological transformation of which the fractal dimensions with corresponding interslipface angles are computed. This exercise has relevance to test the Validity of the model by
considering various time series sand dune data that can be retrieved from the robust satellite remote sensing sensors.
Photosynthesis as a discrete biochemical process
Authors: Štetina M. , KrempaskÝ J.
Published: January 2006

It is shown that the existence of a multioscillatory and chaotic regime observed in the photosynthesis could be explained on the basis of logistic equations, i.e., using a discrete approach. Transforming known phenomenological differential equations describing the photosynthesis into the discrete formalism it is possible to demonstrate that by change of control parameters such equations generate the very well known Feigenbaum‘s scenario of the duplication of states including the possibility of the transition into a chaotic regime. The multioscillatory states characterised by even, and what is surprising, also by odd number of “subcycles” are generated at some special combinations of values of control parameters.
Unveiling uncertain forces in second‐order driven oscillators via internal model: A discrete‐time feedback
Authors: Femat R. , Jiménez-gallegos C.
Published: January 2006

Unveil uncertain forces acting into (or onto) systems is a very interesting and old problem. Indeed, a lot effort has been devoted to develop procedures which results in the understanding of the uncertain forces and its effects. This contribution deals with
recovering of the dynamics of the uncertain forces from measurements (time series). The main idea is to construct an internal model of the nonlinear system and design a discretetime feedback in such way that the model/system differences be stabilized at origin. In principle, if the internal model tracks the trajectory of the nonlinear system, then the uncertain force is recovered by the stabilizing command.
Differential representations of dynamical oscillator symmetries in discrete Hilbert space
Authors: Ruffing Andreas
Published: January 2006

As a very important example for dynamical symmetries in the context of q‐generalized quantum mechanics the algebra aa† − q−2a†a = 1 is investigated. It represents the oscillator symmetry SUq(1, 1) and is regarded as a commutation phenomenon of the q‐Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q‐Hermite functions and systems of creation and annihilation operators are derived. The classical limit q → 1 is investigated. Finally the SUq(1, 1) algebra is represented by the dynamical variables of the q‐Heisenberg algebra.
Staircase baker′s map generates flaring‐type time series
Authors: Radons G. , Hartmann G. C. , Diebner H. H. , Rossler O. E.
Published: January 2006

The baker’s map, invented by Eberhard Hopf in 1937, is an intuitively accesible, two‐dimensional chaos‐generating discrete dynamical system. This map, which describes the transformation of an idealized two‐dimensional dough by stretching, cutting and piling, is non‐dissipative. Nevertheless the “x” variable is identical with the dissipative, one‐dimensional Bernoulli‐shift‐generating map. The generalization proposed here takes up ideas of Yaacov Sinai in a modified form. It has a staircase‐like shape, with every next step half as high as the preceding one. Each pair of neighboring elements exchanges an equal volume (area) during every iteration step in a scaled manner. Since the density of iterated points is constant, the thin tail (to the right, say) is visited only exponentially rarely. This observation already explains the map′s main qualitative behavior: The “x” variable shows “flares”. The time series of this variable is closely analogous to that of a flaring‐type dissipative dynamical system – like those recently described in an abstract economic model. An initial point starting its journey in the tale (or “antenna”, if we tilt the map upwards by 90 degrees) is predictably attracted by the broad left hand (bottom) part, in order to only very rarely venture out again to the tip. Yet whenever it does so, it thereby creates, with the top of a flare, a new “far‐from‐equilibrium” initial condition, in this reversible system. The system therefore qualifies as a discrete analogue to a far‐from‐equilibrium multiparticle Hamiltonian system. The height of the flare hereby corresponds to the momentary height of the H function of a gas. An observable which is even more closely related to the momentary negative entropy was recently described. Dependent on the numerical accuracy chosen, “Poincaré cycles” of two different types (periodic and nonperiodic) can be observed for the first time.
In search of a warning strategy against exchange‐rate attacks: Forecasting tactics using artificial neural networks
Authors: Andreou A. S. , Zombanakis G. A. , Georgopoulos E. F. , Likothanassis S. D.
Published: January 2006

“Heart attacks and devaluations are not predictable and, certainly, are never preannounced”. (The usual remark made by government spokesmen shortly after a domestic currency devaluation has taken place.)

The contribution that this paper aspires to make is the prediction of an oncoming attack against the domestic currency, something that is expected to increase the possibilities of successful hedging by the authorities. The analysis has focused on the Greek Drachma, which has suffered a series of attacks during the past few years, thus offering a variety of such “shock” incidents accompanied by frequent interventions by the authorities. The prediction exercised here is performed in a discrete dynamics environment, based on the daily fluctuations of the interbank overnight interest rate, using artificial neural networks enhanced by genetic algorithms. The results obtained on the basis of the forecasting performance have been considered most encouraging, in providing a successful prediction of an oncoming attack against the domestic currency.
A method for detection of repetitive local effects (RLEs) in discrete recursive processes
Authors: Kelman E. , Shoshany M.
Published: January 2006

One‐dimensional discrete processes, which can be measured repetitively for discrete values of arguments after discrete periodic or non periodic intervals of time, are discussed in this study. These processes can be under effect of different perturbations
with different frequency, amplitudes, with accidental measurement error, etc. The problem investigated, is whether repetitive, local, relatively small effects (RLEs) can be extracted from this data. A simple method for such effects detection is proposed. A model for the simulation of discrete processes with local effects is introduced. Experiments with the method indicate that it is stable in detecting local effects and can
be useful for many applications.
Global properties of symmetric competition models with riddling and blowout phenomena
Authors: Bischi Giant-italo , Gardini Laura
Published: January 2006

In this paper the problem of chaos synchronization, and the related phenomena of riddling, blowout and on–off intermittency, are considered for discrete time competition models with identical competitors. The global properties which determine
the different effects of riddling and blowout bifurcations are studied by the method of critical curves, a tool for the study of the global dynamical properties of two‐dimensional noninvertible maps. These techniques are applied to the study of a dynamic market‐share competition model.
Complex dynamics in a simple model of interdependent open economies
Authors: Yousef Shahriar , Maistrenko Yuri , Popovych Svitlana
Published: January 2006

Based on a simple two‐market model, characterized by a demand link between competitive markets for goods, a system of coupled difference equations is used to represent the interdependent structure of a global economy. Relying on numerical and
analytical approaches, Various dynamic properties of the proposed model are explored. Among others, a general specification of the regions of stability of the equilibrium and main periodic cycles, the transition to chaos through torus destruction, chaotic synchronization, and the coexistence of different types of attractors in parameter space are described. Typical bifurcation processes are illustrated.
Chaos and complexity in a simple model of production dynamics
Authors: Katzorke I. , Pikovsky A.
Published: January 2006

We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one‐dimensional Bernoulli‐type map, and
demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system.
Simulated evolution in a linguistic model
Authors: Knudsen Carsten , Cameron Lynne
Published: January 2006

In this paper we present a simple evolutionary model of childrens’ language development, whose central nonlinearity is represented by noninvertible discrete dynamical systems. The underlying assumption of the model is that children learn from other children through their interactions. The concrete learning mechanism used is based on imitation, where childrens’ languages evolve through attempting to imitate other childrens′ utterances. The use of imitation in evolutionary models has been used, for instance, in evolution of bird song by Kaneko and Suzuki. The model to be presented here is similar to Kaneko and Suzuki’s model, the primary difference being the continuous nature of bird song, in contrast to the discrete nature of childrens’ utterances.
Bifurcation analysis of the Henon map
Authors: Mosekilde Erik , Zhusubaliyev Zhanybai T. , Rudakov Vadim N. , Soukhterin Evgeniy A.
Published: January 2006

Division of the parameter plane for the two‐dimensional Hénon mapping into domains of periodic and chaotic oscillations is studied numerically and analytically. Regularities in the occurrence of different motions and transitions are analyzed. It is shown that there are domains in the plane of parameters, where non‐uniqueness of motions exists. This may lead to abrupt changes of the character of the dynamics under variation in the parameters, that is, to a sudden transition from one stable cycle to another or to chaotization of the oscillations.
Different types of scaling in the dynamics of period–doubling maps under external periodic driving
Authors: Ivank’ov N. Yu. , Kuznetsov S. P.
Published: January 2006

Based on the renormalization group approach developed by Kuznetsov and Pikovsky (Phys. Lett., A140, 1989, 166) several types of scaling are discussed, which can be observed in a neighborhood of Feigenbaum’s critical point at small amplitudes of the driving. The type of scaling behavior depends on a structure of binary representation of the frequency parameter: F‐scaling (Feigenbaum’s) for finite binary fractions, P‐ and Q‐scaling (periodic and quasiperiodic) for periodic binary fractions, and S‐scaling (statistical) for non‐periodic binary fractions. All types of scaling are illustrated by parameter‐plane diagrams for the rescaled Lyapunov exponent.
Type‐II intermittency in a class of two coupled one‐dimensional maps
Authors: Laugesen J. , Mosekilde E. , Bountis T. , Kuznetsov S. P.
Published: January 2006

The paper shows how intermittency behavior of type‐II can arise from the coupling of two one‐dimensional maps, each exhibiting type‐III intermittency. This change in dynamics occurs through the replacement of a subcritical period‐doubling bifurcation in
the individual map by a subcritical Hopf bifurcation in the coupled system. A variety of different parameter combinations are considered, and the statistics for the distribution of laminar phases is worked out. The results comply well with theoretical predictions. Provided that the reinjection process is reasonably uniform in two dimensions, the transition to type‐II intermittency leads directly to higher order chaos. Hence, this
transition represents a universal route to hyperchaos.
Theory of adaptive adjustment
Authors: Huang Weihong
Published: January 2006

Conventional adaptive expectation as a mechanism of stabilizing an unstable economic process is reexamined through a generalization to an adaptive adjustment framework. The generic structures of equilibria that can be stabilized through an adaptive
adjustment mechanism are identified. The generalization can be applied to a broad class of discrete economic processes where the variables interested can be adjusted or controlled directly by economic agents such as in cobweb dynamics, Cournot games, Oligopoly markets, tatonnement price adjustment, tariff games, population control through immigration etc.
The evolution of nonlinear dynamics in political science and public administration: Methods, modeling and momentum
Authors: Kiel L. Douglas
Published: January 2006

This paper examines the evolution of the application of nonlinear dynamics and related methods to the study of political science and public administration throughout the 20th century. Some analysts understood the importance of nonlinearity to political and
administrative studies in the early part of the century. More recently, a growing number of scholars understand that the political and administrative worlds are ripe with nonlinearity and thus amenable to nonlinear dynamical techniques and models. The current state of the application of both discrete and continuous time models in political science and public administration are presented. There is growing momentum in political and public administration studies that may serve to enhance the realism and applicability of these sciences to a nonlinear world.
Stability, instability and complex behavior in macrodynamic models with policy lag
Authors: Asada Toichiro , Yoshida Hiroyuki
Published: January 2006

We construct simple macrodynamic models with policy lag by means of mixed difference and differential equations, and study how lags in policy response affect the macroeconomic (in)stability. Local dynamics of the prototype model are studied analytically, and the global dynamics of the prototype and the extended models are studied by means of numerical simulations. We show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system becomes locally unstable when the policy lag is too long. We also show the existence of cycles and complex behavior in some range of the policy lag.
Statistical analysis of time series with scaling indices
Authors: Atmnaspacher Harald , Ehm Werner , Scheingraber Herbert , Wiedenmann Gerda
Published: January 2006

Statistical techniques based on scaling indices are applied to detect and investigate patterns in empirically given time series. The key idea is to use the distribution of scaling indices obtained from a delay representation of the empirical time series to distinguish
between random and non‐random components. Statistical tests for this purpose are designed and applied to specific examples. It is shown that a selection of subseries by scaling indices can significantly enhance the signal‐to‐noise ratio as compared to that of the total time series.
Bertrand oligopoly revisited
Authors: Puu Tönu
Published: January 2006

This paper reconsiders Bertrand duopoly and oligopoly in the spatial formulation due to Hotelling, 1929. The equilibrium configurations of price and location structure are considered, given elastic demand, and a full dynamics is formulated in order to check for
stability of equilibrium and the possibilities of complex dynamics, such as occurs easily with Cournot oligopoly. The main discussion concerns Hotelling′s original case of two sellers on a given interval, though results for different cases, such as three firms on a circle, and lattices in 2D are indicated.
Nonlinear dynamics in psychology
Authors: Guastello Stephen J.
Published: January 2006

This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and
organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
Analytical investigation of the onset of bifurcation cascade in two logistic‐like maps
Authors: Panchev S.
Published: January 2006

Two modifications of the classical one‐dimensional logistic map are proposed, which permitted analytical study of the onset of the bifurcation (period doubling) cascade. The modified maps are two‐parametric ones. This introduces new features in their behaviour
and makes them more flexible. The results can prove to be useful in the ecological (population dynamics) modeling, where the logistic map is a basic model and also in other fields of application.
Generation of predictive price and trading volume patterns in a model of dynamically evolving free market supply and demand
Authors: Wang J. K.
Published: January 2006

I present a model of stock market price fluctuations incorporating effects of share supply as a history‐dependent function of previous purchases and share demand as a function of price deviation from moving averages. Price charts generated show intervals
of oscillations switching amplitude and frequency suddenly in time, forming price and trading volume patterns well‐known in market technical analysis. Ultimate price trends agree with traditional predictions for specific patterns. The consideration of dynamically evolving supply and demand in this model resolves the apparent contradiction with the Efficient Market Hypothesis: perceptions of imprecise equity values by a world of investors evolve over non‐negligible periods of time, with dependence on price history.
Complexity and state‐transitions in social dependence networks
Authors: Pistolesi Giuliano , Modesti Pierluigi
Published: January 2006

Computation of complexity in Social Dependence Networks is an interesting research domain to understand evolution processes and group exchange dynamics in natural and artificial intelligent Multi‐Agent Systems. We perform an agent‐based simulation by
NET‐PLEX (Conte and Pistolesi, 2000), a new software system able both to build interdependence networks tipically emerging in Multi‐Agent System scenarios and to investigate complexity phenomena, i.e., unstability and state‐transitions like Hopf bifurcation (Nowak and Lewenstein, 1994), and to describe social self organization phenomena emerging in these artificial social systems by means of complexity measures similar to those introduced by Hubermann and Hogg (1986). By performing analysis of complexity in these kind of artificial societies we observed interesting phenomena in emerging organizations that suggest state‐transitions induced by critical configurations of parameters describing the social system similar to those observed in many studies on state‐transitions in bifurcation chaos (Schuster, 1988; Ruelle, 1989).
Asset price dynamics in a financial market with fundamentalists and chartists
Authors: Chairella Carl , Dieci Roberto , Gardini Laura
Published: January 2006

In this paper we consider a model of the dynamics of speculative markets involving the interaction of fundamentalists and chartists. The dynamics of the model are driven by a two‐dimensional map that in the space of the parameters displays regions of invertibility and noninvertibility. The paper focuses on a study of local and global bifurcations which drastically change the qualitative structure of the basins of attraction of several, often coexistent, attracting sets. We make use of the theory of critical curves associated with noninvertible maps, as well as of homoclinic bifurcations and homoclinic orbits of saddles in regimes of invertibility.
The angular distribution of asset returns in delay space
Authors: Koppl Roger , Nardone Carlo
Published: January 2006

Plotting asset returns against themselves with a one‐period lag reveals the “compass rose” pattern of Crack and Ledoit (1996). They describe the pattern, caused by discreteness, as “subjective”. We develop a new and original set of “objective” statistical procedures to quantify the compass rose and detect changes in it. empirical and bootstrapped “theta histograms” permits hypothesis testing. Simulations suggest that intertemporal statistical dependence skews the compass rose in ways that mimic ARCH phenomena. Using our techniques on “credit ruble” data, we test the hypothesis that “Big Players” influence the degree of this “X‐skewing” and, therefore, apparent ARCH behavior.
Detection of the onset of numerical chaotic instabilities by lyapunov exponents
Authors: De Markus Alicia Serfaty
Published: January 2006

It is commonly found in the fixed‐step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that
establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.
On permutation symmetries of hopfield model neural network
Authors: Dong Jiyang , Xu Shenchu , Chen Zhenxiang , Wu Boxi
Published: January 2006

Discrete Hopfield neural network (DHNN) is studied by performing permutation operations on the synaptic weight matrix. The storable patterns set stored with Hebbian learning algorithm in a network without losing memories is studied, and a condition
which makes sure all the patterns of the storable patterns set have a same basin size of attraction is proposed. Then, the permutation symmetries of the network are studied associating with the stored patterns set. A construction of the storable patterns set satisfying that condition is achieved by consideration of their invariance under a point group.
Asymptotic behavior for second order lattice dynamical systems
Authors: Zhou Shengfan
Published: January 2006

We consider the existence of the global attractor for a second order lattice dynamical systems.
Identification of discrete chaotic maps with singular points
Authors: Akishin P. G. , Akritas P. , Antoniou I. , Ivanov V. V.
Published: January 2006

We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.
Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics
Authors: Ruffing Andreas , Windpassinger Patrick , Panig Stefan
Published: January 2006

We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.