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Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
Reverse engineering of complex dynamical networks is important for a variety of fields where uncovering the full topology of unknown networks and estimating parameters characterizing the network structure and dynamical processes are of…
In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.
In this paper, we demonstrate, first in literature known to us, that potential functions can be constructed in continuous dissipative chaotic systems and can be used to reveal their dynamical properties. To attain this aim, a Lorenz-like…
With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…
The article is devoted to the issues of using discrete simulation models for modeling some basic technological processes. In the scientific work, models in the form of multi-agent systems have been investigated, which allow us to consider a…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
Different kinds of models are used to study various natural and technical phenomena. Usually, the researcher is limited to using a certain kind of model approach, not using others (or even not realizing the existence of other model…
The methods of statistical physics of open systems are used for describing the time dependence of economic characteristics (income, profit, cost, supply, currency etc.) and their correlations with each other. Nonlinear equations (analogies…
This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…