Dynamic System

We use a dynamical systems approach to model the origin of bargaining conventions and report the results of a symmetric bargaining game experiment. Our experiment also provides evidence on the psychological salience of symmetry and efficiency. The observed behavior in the experiment was systematic, replicable, and roughly consistent with the dynamical systems approach. For instance, we do observe unequal-division conventions emerging in colmnunities of sylnmetricaily endowed subjects.

1] In the present contribution we focus our attention on the long-term behavior of meandering rivers, a very common pattern in nature. This class of dynamical systems is driven by the coexistence of various intrinsically nonlinear mechanisms which determine the possible occurrence of two different morphodynamic regimes: the subresonant and the superresonant regimes. Investigating the full range of morphodynamic conditions, we objectively compare the morphologic characteristics exhibited by synthetically generated and observed planimetric patterns. The analysis is carried out examining, through principal component analysis, a suitable set of morphological variables. We show that even in the presence of the strong filtering action exerted by cutoff processes, a closer, although not yet complete, similarity with natural meandering planforms can be achieved only by adopting a flow field model which accounts for the full range of morphodynamic regimes. We also introduce a new morphodynamic length scale, L m , associated with spatially oscillating disturbances. Once normalized with this length scale, the relevant morphologic features of the simulated long-term patterns (e.g., the probability density function of local curvature and the geometric characteristics of oxbow lakes) tend to collapse on two distinct behaviors, depending on the dominant morphologic regime.

In a world faced with accelerating climate change, economic instability and resource limits, it is urgent to find better indicators of progress towards sustainability. The available indicators mostly succeed at measuring unsustainable trends that can be targeted by management action, but fall short of defining or ensuring sustainability. A recent review of environmental assessment and reporting at the national level for the United Nations Environment Programme shows about half of reporting countries to be using indicators and provides some lessons learned. However indicators at the national level are not sufficient. The challenges ahead include finding indicators of change in dynamic systems, establishing sustainability targets towards which national progress can be measured, developing global level indicators of planetary sustainability, and providing individuals with indicators reflecting their own progress and providing positive incentives for further efforts. Finally, since achieving sustainability is fundamentally an ethical challenge, a new set of values-based indicators is required to measure and motivate the implementation of ethical principles necessary to guide the transition towards sustainability.

We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Li\'enard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincar\'e problem for some families is also approached.

This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples equally spaced in the frequency domain. The Fast Fourier Transform (FFT) algoritm allows us an effective computation, and it can be applied to a relatively short time series. DFT representation requirements were analized and applied for determining the order-chaos transition in a nonlinear system described by the equation $x[n+1]=rx[n](1-x[n])$. Its effectiveness was demonstrated by comparing the results with those obtained by calculating the largest Lyapounov exponent for the time series set, obtained from the logistic equation.

We show that states of a dynamical system can be usefully represented by multi-step, action-conditional predictions of future observations. State representations that are grounded in data in this way may be easier to learn, generalize better, and be less dependent on accurate prior models than, for example, POMDP state representations. Building on prior work by Jaeger and by Rivest and Schapire, in this paper we compare and contrast a linear specialization of the predictive approach with the state representations used in POMDPs and in k-order Markov models. Ours is the first specific formulation of the predictive idea that includes both stochasticity and actions (controls). We show that any system has a linear predictive state representation with number of predictions less than or equal to the number of states in its minimal POMDP model.

This paper explores the self-organising principles of horizontally-integrated innovation networks. It is shown that such networks can self-organising in environments where the co-ordination and production of new knowledge is itself a complex, dynamic and highly non-linear processes. The paper argues the development of a self-organisation perspective of innovation networks has two advantages. First, it provides a general framework of dynamic systems in which different strands of a highly fragmented literature can be drawn together. Second, formal self-organisation modelling techniques can provide interesting new insights into the micro-macro processes driving dynamic innovation systems.

We address scaling of the "dynamic systems" approach for robot planning to multi-agent cooperation. To accommodate this extension it is necessary to carefully consider how individual behaviors contribute to the vector field. To avoid spun"ous minima and related pro biems a competition dynamics is introduced and its stability is analyzed. A system of two cooperating agents is designed, and examples are presented to illustrate the utility of this approach.

Providing technology support for older people offers distinct challenges for social and IT systems delivery. The definition and integration of services, the diversity of supply, variance in structures, and the lack of centralised control, introduce significant challenges. These challenges stretch contemporary methods in the social and IT domains. In this paper, we introduce a method that we have developed and used successfully over a number of years. We briefly introduce a protocol and framework that utilises the Unified Modelling Language and adapts best practice from methods such as the Unified Software Development Method, the Dynamic System Development Method, and user-centred approaches from the care sector such as Userfit.

A consistent description of a shear flow, the accompanied viscous heating, and the associated entropy balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the temperature distributions. In an appropriate macroscopic limit their transport equations go over into the Navier-Stokes and the heat conduction equation of viscous flows. The inclusion of an artificial heat sink can stabilize steady states with constant temperatures. It mimics a thermostating algorithm used in non-equilibrium molecular-dynamics simulations.

It has been veri"ed that a controllable series capacitor with a suitable control scheme can improve transient stability and help to damp electromechanical oscillations. A question of great importance is the selection of the input signals and a control strategy for this device in order to damp power oscillations in an e!ective and robust manner. Based on Lyapunov theory a control strategy for damping of electromechanical power oscillations in a multi-machine power system is derived. Lyapunov theory deals with dynamical systems without inputs. For this reason, it has traditionally been applied only to closed-loop control systems, that is, systems for which the input has been eliminated through the substitution of a predetermined feedback control. However, in this paper, we use Lyapunov function candidates in feedback design itself by making the Lyapunov derivative negative when choosing the control. This control strategy is called control Lyapunov function for systems with control inputs. Also, two input signals for this control strategy are used. The "rst one is based on local information and the second one on remote information derived by the single machine equivalent method. : S 0 0 0 5 -1 0 9 8 ( 0 1 ) 0 0 0 9 9 -1

The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in space simultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.

Software architecture is a technique which aids the development of complex and dynamic systems. Architecture Description Languages (ADLs) describe software architectures using a textual syntax or a graphical notation. However, not many ADLs have provided ...

Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper, we develop novel tools that can be used within this framework and that are useful for tracking problems. In particular, results for stability analysis of parameterized time-varying discrete-time cascaded systems are given. This class of models arises naturally when one uses an approximate discrete-time model to design a stabilizing or tracking controller for a sampled-data plant. While some of our results parallel their continuous-time counterparts, the stability properties that are considered, the conditions that are imposed, and the the proof techniques that are used, are tailored for approximate discrete-time systems and are technically different from those in the continuous-time context. A result on constructing strict Lyapunov functions from nonstrict ones that is of independent interest, is also presented. We illustrate the utility of our results in the case study of the tracking control of a mobile robot. This application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete-time parameterized systems.

A well-known problem in complex cognition is the so-called dynamic stocks and flows task (DSF). The challenge in this task is to control different flows, e.g. the inflows and outflows of water to a tank, towards a specified goal configuration, i.e. a certain amount of water in the tank. The problem is that some flows are exogenously controlled with a hidden dynamic. These flows need to be counterbalanced by setting endogenous flows. Since the dynamic underlying the hidden flows can be any computable function, this task can be classified as computationally complex. Psychological findings show that humans have difficulties in dealing with such dynamic systems. In this article, we present a formal generalization of this task and present a computational approach for solving such tasks as a first step towards an assistance system for complex system control.

This paper covers stochastic particle methods for the numerical solution of the nonlinear filtering equations based on the simulation of interacting particle systems. The main contribution of this paper is to prove convergence of such approximations to the optimal filter, thus yielding what seemed to be the first convergence results for such approximations of the nonlinear filtering equations. This new treatment has been influenced primarily by the development of genetic algorithms (J. H. Holland , R. Cerf ) and secondarily by the papers of H. Kunita and L. Stettner . Such interacting particle resolutions encompass genetic algorithms. Incidentally, our models provide essential insight for the analysis of genetic algorithms with a non-homogeneous fitness function with respect to time.

A method was proposed in [3] for constructing the equivalent Lagrangian of a non~nservative dynamic system. The method differs from the heuristic method of f'mding a Lagrangian that depends explicitly on time. The goal of the present investigation is to construct the first integral of the system with the use of the Lagrangian proposed in [3]. In contrast to the well-known approaches in [6], where the first integrals were constructed through Lagrangians that depend explicity on time and were obtained earlier in other investigations, here both the fkst integral and the Lagrangian are constructed by the same method with the use of special functions proposed in [6].

We show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales. The temporal "fingerprint" of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scaleinvariant (fractal) structure.

How have connectionist models informed the study of development? This paper considers three contributions from specific models. First, connectionist models have proven useful for exploring nonlinear dynamics and emergent properties, and their role in nonlinear developmental trajectories, critical periods and developmental disorders. Second, connectionist models have informed the study of the representations that lead to behavioral dissociations. Third, connectionist models have provided insight into neural mechanisms, and why different brain regions are specialized for different functions. Connectionist and dynamic systems approaches to development have differed, with connectionist approaches focused on learning processes and representations in cognitive tasks, and dynamic systems approaches focused on mathematical characterizations of physical elements of the system and their interactions with the environment. The two approaches also share much in common, such as their emphasis on continuous, nonlinear processes and their broad application to a range of behaviors.

The spline-based differential quadrature method (SDQM) is applied to the solution of nonlinear initial-value problems. Explicit expressions of weighting coefficients for approximation of derivatives are presented. Dynamic systems with Duffing-type nonlinearity are solved to demonstrate the effectiveness of the method. Numerical results of three examples show that the spline-based differential quadrature method is versatile and stable in the solution of nonlinear initial-value problems. It can be counted on to achieve satisfactory accuracy for long-term integration. r

Service Oriented Architecture (SOA) is an architectural style that is widely used in distributed and dynamic systems. The Service oriented architecture Modeling Language (SoaML) is an OMG standard for modelling SOA independent of a technology. This paper presents a tool for modelling SOA using SoaML and generating OSGi Declarative Services Models from SoaML models. SoaML metamodel has been implemented as an Ecore model using the Eclipse Modeling Framework (EMF). An Eclipse plug-in that allows architects to graphically design SoaML models has been developed using the Graphical Modeling Framework (GMF). We have also implemented a model transformation using ATLAS Transformation Language (ATL) in order to partially generate Declarative Services models. The generated model is used as a Declarative Services Component Description XML specification which is needed to execute code on the OSGi service oriented platform. In this way, we provide SoaML with Model Driven Architecture support.

Insider attacks have the potential to inflict severe damage to an organizations reputation, intellectual property and financial assets. The primary difference between the external intrusions and the insider intrusions is that an insider wields power of knowledge about the information system resources, their environment, policies. We present an approach to detecting abnormal behavior of an insider by applying Dynamical System Theory to the insiders computer usage pattern. This is because abnormal system usage pattern is one of the necessary precursors to actual execution of an attack. A base profile of system usage pattern for an insider is created via applying dynamical system theory measures. A continuous monitoring of the insiders system usage and its comparison with this base profile is performed to identify considerable deviations. A sample system usage in terms of application system calls is collected, analyzed, and graphical results of the analysis are presented. Our results indicate that dynamical system theory has the potential of detecting suspicious insider behavior occurring prior to the actual attack execution.

We present some examples of detailed analysis of intrinsic localized modes in lattices, using the accurate numerical methods derived from the proof of existence of MacKay-Aubry. We report on some improvements on the methods, which are then used to the fullest to obtain the Floquet analysis of the breather solutions. Such calculations are possible taking into account the whole lattice,

In discrete dynamical systems topological entropy is a topological invariant and a measurement of the complexity of a system. In continuous dynamical systems, in general, topological entropy defined as usual by the time one map does not work so well in what concerns these aspects. The point is that the natural notion of equivalence in the discrete case is topological conjugacy which preserves time while in the continuous case the natural notion of equivalence is topological equivalence which allow reparametrizations of the orbits. The main issue happens in the case that the system has fixed points and will be our subject here.

This paper revisits the use of trend forecasting to determine ordering policy in supply chains by viewing it as a part of the control process for making the supply responsive to demand. Trend forecasting is often used to assess demand—a tracked variable in the control context, which drives supply—a tracking variable. Used in this way, it is often observed to increase instability creating the so-called bullwhip effect. Trend is used on the other hand with reliability to increase stability in controller control, but with the difference that a trend of a ...

In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.

We will further develop the study of the dissipation for a Hamilton-Poisson system introduced in \cite{2}. We will give a tensorial form of this dissipation and show that it preserves the Hamiltonian function but not the Poisson geometry of the initial Hamilton-Poisson system. We will give precise results about asymptotic stabilizability of the stable equilibria of the initial Hamilton-Poisson system.

Dynamic systems theories, such as complexity and nonlinear dynamic systems theories, provide increased flexibility in approaching psychological phenomena with a less rigid, more fluid sensibility. They provide us with process language that moves away from linear directionality in construing psychoanalytic action in favor of a sensibility of emergence. This paper situates the concept of mirroring within the realms of systems

The prediction of chaotic time series with neural networks is a traditional practical problem of dynamic systems. This paper is not intended for proposing a new model or a new methodology, but to study carefully and thoroughly several aspects of a model on which there are no enough communicated experimental data, as well as to derive conclusions that would be of interest. The recurrent neural networks (RNN) models are not only important for the forecasting of time series but also generally for the control of the dynamical system. A RNN with a sufficiently large number of neurons is a nonlinear autoregressive and moving average (NARMA) model, with "moving average" referring to the inputs. The prediction can be assimilated to identification of dynamic process. An architectural approach of RNN with embedded memory, "Nonlinear Autoregressive model process with eXogenous input" (NARX), showing promising qualities for dynamic system applications, is analyzed in this paper. The performances of the NARX model are verified for several types of chaotic or fractal time series applied as input for neural network, in relation with the number of neurons, the training algorithms and the dimensions of his embedded memory. In addition, this work has attempted to identify a way to use the classic statistical methodologies (R/S Rescaled Range analysis and Hurst exponent) to obtain new methods of improving the process efficiency of the prediction chaotic time series with NARX.

In this paper, we study the stability problem of nonlinear dynamical control systems. We consider continuous-time dynamical systems whose nominal part is stable and whose perturbed part (uncertainties) is norm-bounded by a positive function. Under some conditions on the perturbation, by using Lyapunov techniques, we show that the system can be uniformly asymptotically stable by a continuous controller.

In this paper our aim is to show the viability of preserving the hyperbolicity of a master/ salve pair of chaotic systems under different types of nonlinear modifications to its Jacobian matrix. Furthermore, we shall provide evidence to show that linear control methods used to achieve synchronization between master and slave systems are preserved under such transformations. We propose to modify both the coefficients of the Jacobian matrix's associated characteristic polynomial through power evaluation as well as through matrix polynomial evaluation. To illustrate the results we present examples of several well known chaotic and hyperchaotic dynamical systems that have been modified using both methodologies.

Short description: matcont is a graphical Matlab software package for the interactive numerical study of dynamical systems. It allows to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, fold ,flip and torus bifurcation points of limit cycles.

Three experiments elicited phonological speech errors using the SLIP procedure to investigate whether there is a tendency for speech errors on specific words to reoccur, and whether this effect can be attributed to implicit learning of an incorrect mapping from lemma to phonology for that word. In Experiment 1, when speakers made a phonological speech error in the study phase of the experiment (e.g. saying ''beg pet" in place of ''peg bet") they were over four times as likely to make an error on that same item several minutes later at test. A pseudo-error condition demonstrated that the effect is not simply due to a propensity for speakers to repeat phonological forms, regardless of whether or not they have been made in error. That is, saying ''beg pet" correctly at study did not induce speakers to say ''beg pet" in error instead of ''peg bet" at test. Instead, the effect appeared to be due to learning of the error pathway. Experiment 2 replicated this finding, but also showed that after 48 h, errors made at study were no longer more likely to reoccur. As well as providing constraints on the longevity of the effect, this provides strong evidence that the error reoccurrences observed are not due to item-specific difficulty that leads individual speakers to make habitual mistakes on certain items. Experiment 3 showed that the diminishment of the effect 48 h later is not due to specific extra practice at the task. We discuss how these results fit in with a larger view of language as a dynamic system that is constantly adapting in response to experience.

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state-variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. Thus, two analytical methods to incorporate state-variable inequality con straints into the Kalman filter are now derived. The first method is a general technique that uses hard constraints to enforce inequalities on the state-variable estimates. The resultant filter is a com bination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate those state variables that are known to vary slowly with time.

The use of dynamical system techniques, optimization methods and statistical algorithms to estimate the characteristics of brain electrical activity are explored. A system approach for characterizing EEG (electroencephalogram) signals, based on nonlinear estimation of dynamical characteristics and modeling the evolution of dynamical processes over time is applied. The dynamical characteristics can be used to better visualize the “state vector” of epileptic EEG signals and for the purpose of pattern recognition. An optimization method for reconstructing parameter spaces of dynamical systems is applied to systems with one or more hidden variables, and can be used to reconstruct maps or differential equations of the brain dynamics. The methods are illustrated by using numerically generated data and EEG data from epileptic patients.

We study the orbit equivalence relation R s for dynamical systems (I, s) arising from piecewise linear maps s: I ! I on the interval I = [0, 1]. Under regularity conditions, we prove that the crossed product von Neumann algebra L 1 (I) · R s is the type III k hyperfinite factor where k 2 ]0, 1] is determined by the subgroup of R þ generated by {m(s(I i ))/m(I i )}, with the I i 's being the underlying partitioning intervals for s and m the Lebesgue measure. Thus we compute the complete invariant for the orbit structures of these maps.