Class Of Dynamic Models Research Articles

A Delayed Dynamical Model Describing the Effect of Tumor-Induced Vascular Endothelial Growth Factor on Angiogenesis: Backward Bifurcations and Global Dynamics

Dynamic models have been successfully used for the prediction of long-term evolutionary behavior of the growth of tumor cells. In this paper, based on previous research, time delay in the process of the growth of tumor cells is further considered and a class of dynamic models with two-time delays and general functional response function is proposed. This model describes the effect of tumor-induced vascular endothelial growth factor (VEGF) on angiogenesis. First, the model is reduced to a two-dimensional one by means of the quasi-steady-state approximation method. This model has forward and backward bifurcations of the equilibria. Then, local stability of all equilibria, global stability of the tumor cell-free equilibrium and the vascular endothelial cell-free equilibrium, and the persistence of this model are studied in detail. It is found that time delay of tumor-induced vascular endothelial cells proliferation does not change local stability of the equilibria, while time delay associated with the growth of tumor cells can lead to the existence of Hopf bifurcation periodic solutions.

Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

We prove existence of time consistent equilibria in a class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applications. Our generalized Bellman equation method identifies and separates both: recursive and strategic aspects of the equilibrium problem and allows to determine the sufficient assumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent equilibrium) in a deterministic model of consumption-saving with beta-delta discounting and its generalized versions involving non-additive payoffs, general form certainty equivalents, as well as stochastic semi-hyperbolic and hyperbolic discounting models (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.

Likelihood-based quantile autoregressive distributed lag models and its applications

ABSTRACTTime lag effect exists widely in the course of economic operation. Some economic variables are affected not only by various factors in the current period but also by various factors in the past and even their own past values. As a class of dynamical models, autoregressive distributed lag (ARDL) models are frequently used to conduct dynamic regression analysis. In this paper, we are interested in the quantile regression (QR) modeling of the ARDL model in a dynamic framework. By combining the working likelihood of asymmetric Laplace distribution (ALD) with the expectation–maximization (EM) algorithm into the considered ARDL model, the iterative weighted least square estimators (IWLSE) are derived. Some Monte Carlo simulations are implemented to evaluate the performance of the proposed estimation method. A dataset of the consumption of electricity by residential customers is analyzed to illustrate the application.

On the Solution of High-Dimensional Macro Models with Distributional Channels

Importance of distributional channels in macroeconomic dynamics has been the object of considerable attention in empirical studies. Despite significant amount of effort aimed at incorporating heterogeneity into macroeconomics, however, their explicit inclusion in the standard policy toolbox is far from widespread. A relevant obstacle, in such cases, is the computation of equilibria. I propose a global solution method for the computation of infinite-horizon, heterogeneous agent macroeconomic models with aggregate uncertainty. Details of the algorithm are illustrated by presenting its application to a an example model: in it, aggregate dynamics depends explicitly on firm entry and exit, and individual choices are often constrained by a form of market incompleteness. Existing computational strategies are either unfeasible or provide inaccurate solutions. Moreover, global solutions are computationally expensive because the minimal representation of the aggregate state space - and thus the aggregate law of motion - faces the curse of dimensionality. The proposed strategy thus combines adaptive sparse grids with a cross-sectional density approximation, and introduces a framework for solving the more general class of dynamic models with firm or household heterogeneity accurately.

A class of dynamic models describing microbial flocculant with nutrient competition and metabolic products in wastewater treatment

In this paper, based on the related theories of microbial continuous culture, fermentation dynamics, and microbial flocculant, a class of dynamic models which describe microbial flocculant with resource competition and metabolic products in wastewater treatment is proposed. By analyzing the global dynamic properties of the model, the feasibility of employing microbial metabolites as flocculant to remove harmful microorganisms is considered.

Equivalent Dynamic Models

ABSTRACTEquivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.

Spatial self-organization in hybrid models of multicellular adhesion.

Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically cellular automata or reaction-diffusion systems. A different class of dynamical processes involves the correlated movement of agents over space, which can be mediated through chemotactic movement or minimization of cell-cell interaction energy. A classic example of the latter is given by the formation of spatially segregated assemblies when cells display differential adhesion. Here, we consider a new class of dynamical models, involving cell adhesion among two stochastically exchangeable cell states as a minimal model capable of exhibiting well-defined, ordered spatial patterns. Our results suggest that a whole space of pattern-forming rules is hosted by the combination of physical differential adhesion and the value of probabilities modulating cell phenotypic switching, showing that Turing-like patterns can be obtained without resorting to reaction-diffusion processes. If the model is expanded allowing cells to proliferate and die in an environment where diffusible nutrient and toxic waste are at play, different phases are observed, characterized by regularly spaced patterns. The analysis of the parameter space reveals that certain phases reach higher population levels than other modes of organization. A detailed exploration of the mean-field theory is also presented. Finally, we let populations of cells with different adhesion matrices compete for reproduction, showing that, in our model, structural organization can improve the fitness of a given cell population. The implications of these results for ecological and evolutionary models of pattern formation and the emergence of multicellularity are outlined.

Network cohesion

We define a measure of network cohesion and show how it arises naturally in a broad class of dynamic models of endogenous perpetual growth with network externalities. Via a standard growth model, we show why network cohesion is crucial for conditional convergence and explain that as cohesion increases, convergence is faster. We prove properties of network cohesion and define a network aggregator that preserves network cohesion.

Determination of the class of dynamic models of target operations

Existing classes of models of operations are limited to the class of accounting models. As a basis for the research, a simple model of the target operation was used. Expert estimates of input products of the operation are reduced in this model to the start time, and expert estimates of output products of the operation - to the time of its completion. The well-known class of operations provides the possibility of compact storage of information in a database and identification of these operations. However, as the experience of the studies showed, these models could not be used to develop the efficiency indicator. To overcome this restriction, the class of dynamic models of target operations was identified. The class of models of system operations, in which the input and output of the operation products are reduced to comparable measures, and the dynamics of the bound state of product operations is determined on the whole range of research, is defined in the paper as the class of dynamic models of target operations. The results of research of test operations using the comprehensive profitability indicator, which was obtained using the features of the dynamic model have shown that such indicator can solve the problems of identification in the area, formerly the part of the area of restrictions for conventional economic indicators.

Relating Latent Change Score and Continuous Time Models

The primary goal of this article is to demonstrate the close relationship between 2 classes of dynamic models in psychological research: latent change score models and continuous time models. The secondary goal is to point out some differences. We begin with a brief review of both approaches, before demonstrating how the 2 methods are mathematically and conceptually related. It will be shown that most commonly used latent change score models are related to continuous time models by the difference equation approximation to the differential equation. One way in which the 2 approaches differ is the treatment of time. Whereas there are theoretical and practical restrictions regarding observation time points and intervals in latent change score models, no such limitations exist in continuous time models. We illustrate our arguments with three simulated data sets using a univariate and bivariate model with equal and unequal time intervals. As a by-product of this comparison, we discuss the use of phantom and definition variables to account for varying time intervals in latent change score models. We end with a reanalysis of the Bradway–McArdle longitudinal study on intellectual abilities (used before by McArdle & Hamagami, 2004) by means of the proportional change score model and the dual change score model in discrete and continuous time.

DETERMINING THE NUMBER OF REGIMES IN MARKOV SWITCHING VAR AND VMA MODELS

We give stable finite‐order vector autoregressive moving average (p * ,q * ) representations for M‐state Markov switching second‐order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p * and q * are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving‐average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our classes of time series include every M‐state Markov switching multi‐variate moving‐average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997) and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoïan (2001) for our classes of dynamic models. A Monte Carlo experiment and an application on foreign exchange rates complete the article. Copyright © 2013 John Wiley & Sons, Ltd.

Steady-state properties in a class of dynamic models

We characterize the location, stability and approach-time of optimal steady states in single-state, infinite-horizon, autonomous models by means of a simple function of the state variable, defined in terms of the model's primitives. The method does not require the solution of the underlying dynamic optimization problem. Its application is illustrated in the context of a generic class of resource management problems.

Bayesian dynamic probit models for the analysis of longitudinal data

The authors consider a dynamic probit model where the coefficients follow a first-order Markov process. An exact Gibbs sampler for Bayesian analysis is presented for the model using the data augmentation approach and the forward filtering backward sampling algorithm for dynamic linear models. The authors discuss how our approach can be used for dynamic probit models as well as its generalizations including Markov regressions and models with Student link functions. An approach is presented to compare static and dynamic probit models as well as for Markov order selection in these classes of dynamic models. The developed approach is implemented to some actual data.

Determining the Number of Regimes in Markov Switching VAR and VMA Models

We give stable finite order VARMA(p*; q*) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p* and q* are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our class of time series include every M-state Markov switching multivariate moving average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997), and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoian (2001) for our classes of dynamic models. Data simulations and an application on foreign exchange rates complete the paper.

Indivisible Investments Under Missing Credit Markets

In the paper I give full characterization for the class of dynamic models with indivisible investments, when credit markets are missing. I introduce an optimal share rule of total savings from the two available technologies that allows to reduce the dimension of the model and apply to the results from the nonconvex optimal growth literature. In the linear technology, a steady state in the differentiable region is almost never obtained. The findings in the program with concave technology turn to be regular, thanks to the technique we use to reduce the number of controls.

Approximate solution of homotopic mapping for nonlinear vibration problem of transmission line

A class of dynamical model for the nonlinear vibration of a transmission line is studied. Using the homotopy mapping method, the approximate solution with an arbitrary degree of accuracy is obtained.

Limiting the parameter search space for dynamic models with rational kinetics using semi-definite programming

Estimation of kinetic parameters is a key step in modelling, as direct measurements are often expensive, time-consuming or even infeasible. The class of dynamic models in polynomial form is particularly relevant in systems biology and biochemical engineering, as those models naturally arise from modelling biochemical reactions using for instance mass action, Michaelis-Menten or Hill kinetics. Often the parameters are not uniquely identifiable for a given model structure and measurement set. Thus the question of which parameters are consistent or inconsistent with the data arises naturally. Here we present a method capable of proving inconsistency of entire parameter regions with the data. Based on the polynomial representation of the system, we formulate a feasibility problem that can be solved efficiently by semi-definite programming. The feasibility problem allows us to check consistency of entire parameter regions by using upper and lower bounds on the parameters. This drastically limits the search space for subsequent parameter estimation methods. In contrast to similar approaches in the literature, the here presented approach does not require a steady state assumption. Measurements at discrete time points are used, but neither regular sampling intervals, nor a time discretisation of the system is required. Measurement uncertainties are dealt with using upper and lower bounds on the measured states.

Saturation in autoregressive models

In this paper, we extend the impulse saturation algorithm to a class of dynamic models. We show that the procedure is still correctly sized for stationary AR(1) processes, independently of the number of splits used for sample partitions. We derive theoretical power when there is an additive outlier in the data, and present simulation evidence showing good empirical rejection frequencies against such an alternative. Extensive Monte Carlo evidence is presented to document that the procedure has good power against a level shift in the last rT% of the sample observations. This result does not depend on the level of serial correlation of the data and does not require the use of a (mis-specified) location-scale model, thus opening the door to an automatic class of break tests that could outperform those of the Bai-Perron type.

Dynamics of Sequential Decision Making

We suggest a new paradigm for intelligent decision-making suitable for dynamical sequential activity of animals or artificial autonomous devices that depends on the characteristics of the internal and external world. To do it we introduce a new class of dynamical models that are described by ordinary differential equations with a finite number of possibilities at the decision points, and also include rules solving this uncertainty. Our approach is based on the competition between possible cognitive states using their stable transient dynamics. The model controls the order of choosing successive steps of a sequential activity according to the environment and decision-making criteria. Two strategies (high-risk and risk-aversion conditions) that move the system out of an erratic environment are analyzed.

The Possibility of Cyclical Behavior in a Class of Dynamic Models

The study investigates conditions under which endo genous cyclic behavior may be observed within the context of Predator-Prey (Lotka -Volterra) Models. The analysis also establishes conditions under which such behavior is non-existen t and hence establishes conditions for global convergence to the interior equilibrium, whenever i t exists. The results are then applied to two diverse sets of economic exercises and shows how th e conclusions of those exercises may be established under a much weaker set of assumptions. Based on these discussions, a numerical example of robust periodic behavior is provided.