Discrete Dynamics in Nature and Society

https://www.hindawi.com/journals/ddns

List of Papers (Total 9,752)

Chaos: Challenges from and to socio-spatial form and policy

A brief assessment is given of the major accomplishments made through the mathematics of chaos to the understanding of socio-spatial dynamics to date. Certain shortfalls are also presented, mostly associated with model testing and falsifiability which transcend socio-spatial dynamics. Beyond such shortcomings, lie an array of challenges for chaotic dynamics involving specifically...

Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems

A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between the π-theorem of the theory of dimensionality, the second law of thermodynamics and the stoichiometry of complex physicochemical reactions, basic dynamic equations and an extreme principle were formulated. The meaning of discrete time and space in the...

Collision patterns on mollusc shells

On mollusc shells one can find famous patterns. Some of them show a great resemblance to the soliton patterns in one-dimensional systems. Other look like Sierpinsky triangles or exhibit very irregular patterns. Meinhardt has shown that those patterns can be well described by reaction–diffusion systems [1]. However, such a description neglects the discrete character of the cell...

Sociodynamics applied to the evolution of urban and regional structures

The article consists of two parts. In the first section the concepts of sociodynamics are briefly explained. Sociodynamics is a general modelling strategy for the quantitative description of dynamic processes in the human society. The central concepts of sociodynamics include transition rates depending on dynamic utilities and the master equation for the probability distribution...

Universality of oscillation theory laws. types and role of mathematical models

The universality of oscillation theory laws is discussed. It is suggested that all models of concrete systems be separated into four categories: models – “portraits” of investigated systems, models of the type of “black box”, aggregating models, and models of certain phenomena which can occur in real systems. As an example of the model of the fourth type, the equation of...

Nonlinearity in social dynamics – order versus chaos

This paper discusses the significance of applying nonlinear theory to examine the complexity of social and economic evolution. First, we generally examine possible implications of nonlinear theory for analyzing the complexity of human societies. Second, we select two socio-economic models to illustrate our viewpoints.

Active stabilization of a chaotic urban system

A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. The key conception of the method is based on parametric perturbation. This means that the equations of motion are influenced by continuous variation of some selected parameters. Thus – without using any external forces – the motion of the system...

Ergodic cobweb chaos

This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output constraints and the dynamics of the modified model. Due to the upper and lower bounds, a transitional function takes on a tilted z-profile having three piecewise segments with two turning points. It prevents the...

Fixed points of log-linear discrete dynamics

In this paper we study the fixed points of the Log-linear discrete dynamics. We show that almost all Log-linear dynamics have at most two fixed points which is a generalization of Soni's result.

Synchronization of spatiotemporal chaos using nonlinear feedback functions

Synchronization of spatiotemporal chaos is studied using the method of variable feedback with coupled map lattices as model systems. A variety of feedback functions are introduced and the diversity in their choices for synchronizing any given system is exemplified. Synchronization in the presence of noise and with sporadic feedback is also presented.

Endogenous oscillations in a discrete dynamic model with inventory

Introducing the producer's intertemporal optimizing behavior, we extend the Eckalbar Disequilibrium Macro-Model (1985) and reconsider the dynamic features of the modified model. We concern ourselves with the existence of inventory cycles when the expectations are formed adaptively. The endogenous inventory cycle is detected using the Hopf bifurcation theorem in which a...

Well-posedness of difference elliptic equation

The exact with respect to step h∈(0,1] coercive inequality for solutions in Ch of difference elliptic equation is established.

About chaotization mechanisms of the distributed dynamical systems which are close to discrete

The investigations of stochastization mechanisms of distributed dynamical systems (DDS) are developed not so complete as stochastization of dynamical systems with concentrated parameters (CDS). Therefore the corresponding DDS which is close (in one or other sense) to the CDS under consideration is used. Such substitution means some roughening of an initial problem. However, there...

Predictability problems of global change as seen through natural systems complexity description. 1. General Statements

The overall problem of global change is considered as the mathematical discrete dynamics discipline that deals with the sets, measures and metrics (SMM) categories in information sub-spaces. The SMM conception enables to unify techniques of data interpretation and analysis and to explain how effectively the giant amounts of information from multispectral satellite radiometers and...

Nonlinear feedback control of spatiotemporal chaos in coupled map lattices

We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the...

Dynamic system evolution and markov chain approximation

In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a...

Irregular Attractors

In this paper the definition of attractor of a dissipative dynamical system is introduced. The classification of the existing types of attractors and the analysis of their characteristics are presented. The discussed problems are illustrated by the results of numerical simulations using a number of real examples that provides the possibility to understand easily the main...

Morphometric relations of fractal-skeletal based channel network model

A fractal-skeletal based channel network (F-SCN) model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these...

Some remarks on second order linear difference equations

We obtain some further results for comparison theorems and oscillation criteria of second order linear difference equations.

Nonlinear dynamics of the additive-pulse modelocked laser

We have modeled the additive-pulse modelocked (APM) laser with a set of four nonlinear difference equations, that describe the transit of optical pulses through the main cavity and through an external cavity containing a single-mode optical fiber. Simulating the system under several parameter variations, including fiber length, gain, and fiber coupling, we have observed period...

Cities and cellular automata

Cellular automata provide a high-resolution representation of urban spatial dynamics.Consequently they give the most realistic predictions of urban structural evolution, and in particular they are able to replicate the various fractal dimensionalities of actual cities. However, since these models do not readily incorporate certain phenomena like density measures and long-distance...