Discrete dynamics

Discrete dynamics. , discrete dynamical systems. ØA discrete event occurs at an Jul 20, 2020 · The Python interface is based on these templates and the Matlab interface supports this workflow as a way to go embedded. pdf. In this variant, there is only one temperature threshold, and to avoid chattering the thermostat simply leaves the heat on or off for at least a fixed amount of time. In general, we assume that such a rule can be represented by a function. Aeshah A. May 15, 2024 · In this work, the industrial application and numerical simulation on the discrete dynamics of fine PMs are studied, such as condensational growth, deposition and agglomeration. The main objective of Discrete Dynamics in Nature and Society is to foster links between basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. 1-1 Retracted: Deep Learning-Based Detection and Identification Method for Sports Health Video Dissemination. [1] The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness function to incorporate the This book is to serve as a text for engineering students at the senior or beginning graduate level in a second course in dynamics. Carnegie Mellon University in Qatar If a company only produces simple products, production can be scheduled manually with the correct bill of materials (BOM) parts arriving on the production floor, at the correct time, and at the proper resource. A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. Accomplished In classical mechanics, dynamics can be described by parameterized paths in phase Feb 15, 2018 · As we all know, there are a great number of optimization problems in the world. There is also Dynamic Systems (DS) field, but it stays a bit aside as it is used to model Discrete Dynamical Systems. In recent years, a series of novel numerical algorithms, chemo-mechanical frameworks, and May 18, 2024 · Relationship between the Significant Solutions of Static Traffic Assignment Problems for Mixed Traffic Flow of Connected and Automated Vehicles and Human-Driven Vehicles. The DDS is said to be finite if X is finite. DMD simulations are computationally more efficient than continuous Nov 1, 2018 · 3. - Research Article. First, a model is proposed to Mar 29, 2021 · With the application of the particle damping technology to cable vibration attenuation, the rootless cable damper overcomes the limit in installation height of existing dampers. Dynamical systems are about the evolution of some quantities over time. Using in vivo two-photon calcium imaging in the auditory cortex of mice, we show that local network It is shown that during the delay epoch, the activity of ALM neurons moved towards discrete end points that correspond to specific movement directions that were robust to transient shifts in ALM activity caused by optogenetic perturbations. com: Books Skip to main content Jun 15, 2023 · Among these approaches, 3D discrete dislocation dynamics (3D-DDD) emerges as a powerful physics-based numerical tool that can be applied to perform accurate micron-scale simulations at affordable cost [25], [26], [27]. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. A. 1. Advance Praise by Stuart Kauffman. 2) is the constant factor by which the population is augmented at each 1. Crack propagation: discrete crack dynamics (DCD) Discrete crack dynamics, a new tool to study fracture in brittle materials, is developed based on four postulates: (i) each crack can be modelled as a collapsed zero-stiffness inclusion, (ii) crack growth is incremental and quasi-static, (iii) crack growth can be modelled by introducing a small crack (or pseudo-inclusion) ahead of the the dynamics (with a focus on coherent Ising machines (CIMs)) and structure of the coupling network in determining the success of sol- ving the discrete Ising problem. RONALD L. (This is one of several things known as a “discrete dynamical system” in mathematics. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. 1-14 Climate Change Vulnerability and Key Adaptation Trajectory of the Regional Economic System. Our results show that discrete attractor dynamics underlie short-term memory related to motor planning. Short-term memories link events separated in time, such as past sensation and future actions. Rather than using costly time integration methods that take the largest Dec 1, 2023 · On the other hand, planar (2D) dislocation dynamics, often referred to as discrete dislocation plasticity (DDP), is computationally faster and inherently flexible with respect to boundary conditions and the inclusion of microstructures, hence can be used to solve more complicated boundary value problems that may otherwise be inaccessible to 3D Discrete and Continuous Dynamical Systems(DCDS) publishes peer-reviewed original and expository papers on the theory, methods and applications of analysis, differential equations and dynamical systems. Consider a variant of the thermostat of example 3. In the initial state, if the temperature is less than or equal to 20 Jun 1, 2023 · Discrete Dynamics in Nature and Society published special issues feature collections of articles based around a common theme, author or event Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. Expand. 21 Nov 2022. 18 May 2024. - Article ID 6039594. Moreover, in presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. Dynamic vehicle routing problem (DVRP) is a major variant of VRP, and it is closer to real logistic scene. Hong Li | Xian Zhang. AT & T Laboratories, Florham Park, New Jersey, U. Apr 1, 2014 · 2. Jaewoong Yun. In this article, we propose a continuous Jul 1, 2016 · EXPLORING DISCRETE DYNAMICS (second edition) is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (www. Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. For more background information, look for “code generation” in our paper. Set the initial condition to x(0) = 0. GRAHAM. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic Algebraic Dynamics Berkeley, 10 May 2012 - 13 May 2012. Discrete Dynamics are supported from the C part of acados, but this option has indeed not been added to the interfaces yet. For example, many ecological models are discrete dynamical systems, with the most famous being the logistic map: May 10, 2001 · A mathematical formulation is developed to model the dynamics of sand dunes. Discrete Dynamics in Nature and Society + Journal Menu. The journal intends to stimulate publications directed to the analyses of computer generated solutions and chaotic in particular Jun 25, 2018 · Abstract. That is, the function's domain is an uncountable set. The identification of macrostates for the MSM is a central decision that impacts the quality of the MSM but depen … Oct 1, 2021 · In this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We study the discrete model for cooperation as expressed through the dynamics of the family of noninvertible planar maps (x, y) → (x exp(r(1 − x) + sy), y exp(r(1 − y) + sx)), with parameters r, s > 0. Aug 24, 2022 · Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. In this article, a two-dimensional (2D) discrete adaptive synapse-based neuron (DASN) model without external excitation is proposed using Euler’s discretization method. e. 1 Discrete dynamical systems. In DVRP, the customers’ demands appear with time, and the unserved customers’ points must be LeeSeshia_Solutions_2_0. 6. Today almost all numerical integrations of classical dynamics are performed by Newton’s discrete dynamics, by updating the positions at discrete times. It is called the orbit of xof the discrete dynamical system de ned by A. 4xn(1 − xn). We demonstrate the realization of an anti-parity-time (PT)-symmetric photonic lattice in a coherent three-level Λ-type ⁸⁵Rb atomic Mar 15, 2011 · Buy Exploring Discrete Dynamics on Amazon. g. Consider a monopoly, where q is its output, p ( q) = a - bq α the price function ( a, b > 0, α ⩾ 1) and C ( q) = cq β ( c > 0, β ⩾ 2) its cost function. We can rearrange this equation into a form that provides a simple interpretation of ‚: ‚ = Nt+1 Nt (5. 7. Discrete Dynamics in Nature and Society. SD and DE are traditional, AB is relatively new. , a connected interval of the reals ). - Article ID 5622961. ADVISORY EDITORS. As a functional consultant for manufacturing, you need to know how to configure Dynamics 365 Supply Chain Management for discrete manufacturing, so your customer can perform and control Jun 19, 2023 · Discrete nonlinear systems usually have higher implementation efficiency than continuous nonlinear systems, but they can also exhibit dynamics diversity and chaos complex as continuous nonlinear systems. Damping is achieved through energy dissipation by collisions and friction. Abstract. In order to integrate the D-NURBS ordinary differential equations of motion ( 17) in an interactive modeling environment, it is important to provide the modeler or designer with visual feedback about the evolving state of the dynamic model. Discrete Dynamics in Nature and Society -. Volume 2024. Perturbations occasionally switched the population dynamics to the other end point, followed by incorrect actions. ØA discrete systemis one that operates in a sequence of discrete stepsor has signals taking discrete values. 1. S. Iterating gives a sequence of vectors x;Ax;A2x;:::Anx;:::. 31 Dec 2021. Nov 18, 2014 · Molecular Dynamics (MD) computer simulations have become a standard tool for investigating a variety of atomic and molecular systems ranging from solids to simple fluids to complex biomolecular assemblies. The great John von Neumann invented cellular automata. 2024. Journal overview. 2. These simulations have led to significant improvement Aug 24, 2022 · Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Jul 8, 2021 · In this paper, we propose to analyze discrete versions dynamic neural fields based on nearly exact discretization schemes techniques. When Δt = 16, you should get exactly the same numbers as you did above using xn + 1 − xn = 2. These end points were robust to transient shifts in ALM activity caused by optogenetic perturbations. PDF. JAN KAREL LENSTRA Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands. by Discrete Dynamics in Nature and Society. Won, Y. Each Replicator equation. - Article ID 4875909. Journal. Subsection 6. In this article, we present a self-supervised learning approach that actively models the dynamics of May 18, 2024 · Relationship between the Significant Solutions of Static Traffic Assignment Problems for Mixed Traffic Flow of Connected and Automated Vehicles and Human-Driven Vehicles. ) Thus, a DDS is the same as an endomorphism of a set. Thus, we studied the discrete dynamics of cageless ball bearings. In this section we construct a discrete time dynamic model of a monopoly, after determining the profit maximizing output. A discrete time (or, simply, discrete) dynamical system is a rule that, when applied recursively, generates a sequence of numbers or vectors. We determine conditions for a Hopf bifurcation — probably one of a We study discrete opinion dynamics in a social network with "stubborn agents" who in uence others but do However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exists an infinite number of real-valued Hamiltonians for any small value ofτand an infinite number of complex-valued Hamiltonians for any large value ofτ. Monte Carlo simulations are given for illustration. A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (e. Special Issues. Discrete dynamical system. 1 They are particularly attractive for dynamics and for equilibrium sampling in high density condensed matter systems where large scale collective modes may be significant. Recall that a discrete-time dynamical system (or DTDS) describes a sequence of measurements made at equally spaced intervals. This paper examines the dynamic linkages among economic policy uncertainty (EPU), the green bond market, the carbon market, and the macroeconomy using the time-varying parameter vector autoregressive…. In the recent years, Discrete Dislocation Dynamics (DDD) simulation, aiming at simulating the collective motion and interactions of large ensembles of dislocations, has proven to be a powerful tool to study plasticity at small scales [2], [3], [4], [5]. Oct 18, 2021 · The Mechanism Causing an Increase in Farmland Transfer Rent and the Restraining Effect of High Rent on Grain Production. Feb 12, 2024 · Symbolic dynamics provides an alternative view of this process, in which periodic dynamics correspond to a two-state automaton implementing a discrete shift on a symbolic register 109. IECE 553/453–Fall 2019 Prof. Special Issue. In this case, the IES should be modeled as a hybrid system considering the cyber-physical interactions, in which discrete control events are triggered when specific energy states accumulate to a certain extent [22]. Discrete time model. Introduction. (a) Model of a cageless ball bearing with discrete raceways; (b) Projection 6. Journals. Jan 20, 2011 · The classical voter model is generalized by introducing nodes (stubborn agents) that have a fixed state by showing that the presence of stubborn agents with opposing opinions precludes convergence to consensus. A A discrete system is one that operates in a sequence of discrete steps or has signals taking discrete values. A n nmatrix Ade nes a linear transformation T(x) = Ax. - Volume 2021. Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Discrete dynamical behaviour can be found in The continuous time dynamics_x of a system is governed by its current statex. Dola Saha. EDITED_BY : Print ISSN: 1026-0226 Online ISSN: 1607887X. The journal is committed to recording important new methods and results in its field and maintains the highest standards of innovation and quality. These general principles should provide direct construction of difference equations for This is an example of a linear discrete dynamical system. This means that each component of \ (\mathbf {x}\) is a real number. It grew out of many years experience in teaching such a course to senior students in mechanical engineering at the University of California, Berkeley. The proposed model Jun 15, 2016 · EXPLORING DISCRETE DYNAMICS (second edition) is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (DDLab), widely used in research and education. We think of tas time and x(t) as the situation at Exploring Discrete Dynamics - Second Edition The book was published in 2011 by Luniver Press, an 8x10 inch 577 page paperback with color figures, available at Amazon-UK , Amazon-USA, and other online book sellers. When T is taken to be the integers, it is a cascade or a map. 1 is a DTDS because it describes the height of a tree h (the dependent variable) at discrete times t (the independent variable, defined A discrete dynamical system may be based on additional state variables that evolve together in time and whose dynamics are interrelated. Here, we introduce dynamical systems where the state of the system evolves in discrete time steps, i. Volume 2022. We extend the DMD force field by introducing long-range electrostatic interactions to model salt-bridges and a sequence-dependent semiempirical potential accounting for natural tendencies of certain amino acid sequences to Apr 30, 2024 · Definition: Discrete-time dynamical system; Definition: Continuous-time dynamical system; Exercise \(\PageIndex{1}\) Exercise \(\PageIndex{2}\) Dynamical systems theory is the very foundation of almost any kind of rule-based models of complex systems. Oct 25, 2022 · The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball. Short-term memories are correlated with slow neural dynamics May 28, 2021 · Discrete dynamics can be utilized to depict complex behaviour and its evolution in physics, mathematics, biology, engineering, economics, and business. However, the Feb 1, 2022 · The discrete actions of numerous controllers consequently affect the dynamics of energy flows. In each period, adjusting individuals update their action based on the time-lagged information, where the length of delay for each player follows a probability distribution. We prove that the map is proper in the open positive quadrant and describe its various stretching and folding actions. Feb 15, 2018 · 1. When assessing the success of such a model in capturing physical features we monitor morphology, dune growth, dune migration and spatial patterns within a dune field. Discrete Dynamics in Nature and Society aims to elaborate such principles, which are expected to lead to a better understanding of the exact meaning of “discrete” time and space, and, to the creation of a new “calculus” for discrete complex dynamics. Dec 27, 2022 · Dynamical Analysis of Secondary Dengue Viral Infection with Multiple Target Cells and Diffusion by Mathematical Model. Discrete Systems. 5. Introduction to Discrete Dynamical Systems and Chaos. Oct 18, 2012 · Discrete dynamics that emerge in brain networks are believed to be the neuronal correlate of category formation. The discrete Newtonian dynamics has the same invariances as the analytic dynamics, but differs fundamentally by that only the discrete positions are dynamic variables of the discrete time. This meeting will focus on algebraic and arithmetic properties of discrete dynamical systems arising in algebraic geometry though perspectives from various branches of mathematics, such as complex dynamics, valuation theory, arithmetic geometry, mathematical logic, p -adic analysis, et Aug 31, 2016 · In dislocation-mediated plasticity of crystalline materials, discrete dislocation dynamics (DDD) methods have been widely used to predict the plastic deformation in a number of technologically important problems. These collective networks are at the core of complexity and emergent self-organisation. Major Paradigms in Simulation Modeling The major approaches (paradigms) in simulation modeling are shown in the same scale in Figure 3: System Dynamics (SD), “Discrete Event” (DE) and Agent Based (AB). That is, different individuals may be called upon to react to heterogeneous Discrete Dynamics in Nature and Society published special issues feature collections of articles based around a common theme, author or event Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. Mar 14, 2022 · Dynamical systems can be classified according to the nature of time. In the convergence analysis of these algorithms, the deterministic discrete-time (DDT) method can reveal the dynamic behavior of PCA/MCA and GPCA/GMCA algorithms effectively. View on Wiley Online Library. A discrete dynamical system is a system which updates through discrete updates: \[ u_{n+1} = model(u_n,n) \] There are many examples of a discrete dynamical system found throughout the scientific literature. Regarding computational and numerical simulations, discrete-time models are more efficient. A discrete dynamical system is a dynamical system whose state evolves over state space in discrete time steps according to a fixed rule. Discrete dynamical system definition. Discrete dynamical systems can be described using supergeometry. First, a model is proposed to An approach using a discrete-time system is better to describe the tumor dynamics compared to a continuous-time system (when populations have non-overlapping generations). We demonstrate the realization of an anti- parity-time (PT) -symmetric photonic lattice in a coherent three-level Λ-type 85 Rb atomic system both experimentally and theoretically. Suppose that we are studying a system whose state at any given time can be described by a list of numbers: for instance, the numbers of rabbits aged 0,1, and 2 years, respectively, or the number of customers of two different phone companies in Canada. To contrast, a discrete-time signal has a countable domain, like the Jul 26, 2012 · Here we employ discrete molecular dynamics (DMD) simulations with an all-atom force field to fold fast-folding proteins. It consider show systems change over time, not just static properties of observations. In particular, we will discuss conditions for the stability of nontrivial solutions of these models, based on various types of kernels and corresponding parameters. In this paper, a coupled multi-body dynamics—discrete element method is proposed to simulate the damping of the damper—cable system under a Oct 1, 2014 · Discrete dislocation dynamics (DDD) [3, 4, 5] allows to study the e ect of particular mechanisms on the plastic deformation behavior due to dislocation propagation, e. 15 Oct 2021. The physical processes display strong non-linearity that has been taken into account in the model. J. by Dan Liu & Wenfeng Mo & Chuanbin Yin & Paolo Renna. Economics, Environmental Science. Evaluate your Feb 6, 2024 · A lot of Jacobian-based control methods for continuum robots rely on the real-time calculation of the pseudoinverse of time-varying Jacobian matrices, which; however, is not friendly to the hardware implementation of the control system and may be intractable to conventional matrix inversion methods intrinsically designed for time-invariant matrices. Feb 6, 2019 · Neuronal networks involving the frontal cortex follow discrete attractor dynamics to maintain short-term memories over times of seconds, much longer than the time-constant of individual neurons. We study discrete opinion dynamics in a social network with "stubborn agents" who influence others but do not change their opinions. [ 51, 52 ], two kinds of memristive neurons developed from memristor-based neural circuits, which are, respectively, coupled with magnetic flux-dependent and charge-controlled memristors, present adaptive mode transition and selection by regulating its intrinsic parameter under energy levels. Volume 2021. 3 Discrete Dynamics Equations. 01 and type in 0. Jan 31, 2022 · Principal/minor component analysis (PCA/MCA), generalized principal/minor component analysis (GPCA/GMCA), and singular value decomposition (SVD) algorithms are important techniques for feature extraction. The relationship in Warm-Up 1. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Min Liu Rong Huang Yang Lu. Cyber-Physical Systems Discrete Dynamics. The profit of the monopoly is given as Oct 1, 2023 · A two-dimensional discrete dislocation dynamics (DDD) framework is extended to model plastic deformation in polycrystalline materials having realistic grain morphology in finite geometries. May 7, 2012 · In this paper, we examine the role of delays in discrete time evolutionary game dynamics. , how di erent junction Jan 21, 2011 · Discrete molecular dynamics simulations of a-synuclein Discrete step function potentials are used in DMD to define inter-atomic interactions, rather than continuous potentials widely adopted in Oct 1, 2011 · Discrete molecular dynamics (DMD) simulation of hard spheres was the first implementation of molecular dynamics (MD) in history. Such an instantaneously reconfigurable anti- PT -symmetric photonic lattice is “written” by two one-dimensional coupling fields, which are arranged Dec 23, 2020 · Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. Discrete Dynamical Systems. Borns-Weil (MIT) Discrete and Continuous Dynamical Systems May 18, 2014 15 / 32 1-13 Impact of Rule Governance Mechanism on Project Performance in Public Rental Housing PPP Projects: Control Rights as a Moderating Variable. For authors For reviewers For editors Table of Contents. The formulation includes constitutive rules to represent intra-grain dislocation mechanisms as well as dislocation/slip transmission across grain boundaries. For more details, see the introduction to discrete dynamical systems, or for an introduction into the concepts behind dynamical systems in general, see the idea of a 5. . Raezah. Observations of such dynamics have recently been made; however, it is still unresolved if they actually match perceptual categories. 1 Discrete Linear Systems The simplest discrete model is the linear model,1 which we may write as Nt+1 = ‚Nt; (5. Apr 1, 2020 · A new efficient framework coupling the two dimensional (2D) discrete dislocation dynamics (DDD) and the extended finite element method (XFEM) is developed for modeling the dynamic evolution of multiple dislocations in crystalline materials with abundant interfaces/surfaces. In this book we will be mainly considering two classes of dynamical systems, both having a continuous state space. com FREE SHIPPING on qualified orders Exploring Discrete Dynamics: Wuensche, Andrew: 9781905986316: Amazon. WILEY-INTERSCIENCE SERIES IN DISCRETE MATHEMATICS AND OPTIMIZATION. The function itself need not to be continuous. 3. Over the past few decades, discrete dislocation dynamics, a modeling framework allowing for the simulation of the collective motion and interactions of dislocations in crystalline media, has been the subject of intense development worldwide. 2 The first class is called discrete dynamical system. Unit 19: Discrete dynamical systems Lecture 19. 1 Representing Discrete-Time Dynamical Systems. Citation. 1) with ‚ a positive real number and N0 given. DISCRETE DYNAMICS. Zhen Zhang | Pengfei Su. We write x(t) = Atxso that x(0) is the initial condition. The first step is to reproduce the result you got with the above function iteration applet and Δt = 16. DDLab. 15x(1 − x) for the function. We generalize the classical voter model by This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. Jul 21, 2022 · Over the past decade, Markov State Models (MSM) have emerged as powerful methodologies to build discrete models of dynamics over structures obtained from Molecular Dynamics trajectories. Dec 31, 2021 · Approaches to Multiple Attribute Decision-Making with Fuzzy Number Intuitionistic Fuzzy Information and Their Application to English Teaching Quality Evaluation. The independent and combined effects of the WPTA and the WESP on fine PM removal are investigated in a 280 t/h coal-fired power plant. In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. Mar 11, 2024 · In Ref. ØDiscrete= “individually separate / distinct”. ØIt is said to have discrete dynamics. For example, in a predator-prey system, one variable may describe the population size of the predator and the other may describe the prey. Following recent advances, the proposed model is Nov 1, 2023 · Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems. One of the relatively complicated and high-level problems is the vehicle routing problem (VRP). A discrete dynamical system (short: DDS) is a pair ( X, ϕ) of a set X and a map ϕ: X → X . This evolution can occur smoothly over time or in discrete time steps. 1-1 Retracted: Empirical Research on the Relationship between Industry Working Capital Shortfall and Company Cash Holding in the Same Industry. Aug 20, 1999 · Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. wc td qt jz my wp ea cy fu ss