From Dynamical Systems to Complex Systems

2003 ◽  
pp. 141-150
Author(s):  
Giorgio Turchetti
Keyword(s):  
Dynamical Systems ◽  
Complex Systems

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

Data-Driven Methods for Detecting Traffic Jams in Vehicular Traffic Systems

2020 ◽  
Author(s):  
Amin Ghadami ◽  
Charles R. Doering ◽  
Bogdan I. Epureanu
Keyword(s):  
Dynamical Systems ◽  
Complex Systems ◽  
Critical Point ◽  
Traffic Flow ◽  
Traffic Dynamics ◽  
Traffic Jams ◽  
Forecasting Methods ◽  
Traffic Flow Management ◽  
Traffic Systems ◽  
Emergent Behaviors

Abstract Ground vehicle traffic jams are a serious issue in today’s society. Despite advances in traffic flow management in recent years, predicting traffic jams is still a challenge. Recently, novel techniques have been developed in complex systems theory to enable forecasting emergent behaviors in dynamical systems. Forecasting methods have been developed based on exploiting the phenomenon of critical slowing down, which occurs in dynamical systems near certain types of bifurcations and phase transitions. Herein, we explore recently developed tools of tipping point forecasting in complex systems, namely early warning indicators and bifurcation forecasting methods, and investigate their application to predict traffic jams on roads. The measurements required for forecasting are recorded dynamical features of the system such as headways between cars in traffic or density of cars on road. Forecasting approaches are applied to simulated and experimental traffic flow conditions. Results show that one can successfully predict proximity to the critical point of congestion as well as traffic dynamics after this critical point using the proposed approaches. The methodologies presented can be used to analyze stability of traffic models and address challenges related to the complexity of traffic dynamics.

Non-stationary stationarity in systems of third type and philosophy of instability

2015 ◽  
Vol 4 (2) ◽  
pp. 65-74
Author(s):  
Гавриленко ◽  
T. Gavrilenko ◽  
Еськов ◽  
Valeriy Eskov ◽  
Еськов ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Complex Systems ◽  
Biological Systems ◽  
Deterministic Chaos ◽  
Stochastic Approach ◽  
Distribution Functions ◽  
Self Organization ◽  
Deterministic Approach ◽  
The Third ◽  
Specific Assessment

There are several criteria in science for stationarity (stability) of different dynamical systems. The stationarity in physics, engineering and chemistry is being interpreted as matching the requirements of dx/dt=0, where x=x(t) - is the vector of system’s state, or the equality of distribution functions f(x) for different samples which characterize the system. However, in case of social or biological systems the matching of the requirements is impossible and there is a problem of specific assessment of stationary regimes of complex systems of the third type. The possibility of studying of such systems within the frame of deterministic chaos, stochastic approach and theory of chaos and self-organization is being discussed. This article explains why I.R. Prigogine refused from materialistic (in fact deterministic) approach in the description of such special systems of third type and tried to get away from the traditional science in the description of biological systems.

SYMBOLIC DYNAMICS, COARSE GRAINING AND THE MONITORING OF COMPLEX SYSTEMS

2011 ◽  
Vol 21 (12) ◽  
pp. 3465-3475 ◽  
Author(s):  
VASILEIOS BASIOS ◽  
DÓNAL MAC KERNAN
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Error Estimates ◽  
Time Scales ◽  
Symbolic Dynamics ◽  
Prediction Error ◽  
Probabilistic Approach ◽  
Coarse Graining ◽  
Complex Nonlinear Systems

Coarse graining techniques and their associated symbolic dynamics are reviewed with a focus on probabilistic aspects of complex dynamical systems. The probabilistic approach initiated by Nicolis and coworkers has been elaborated. One of the major issues when dealing with the dynamics of complex nonlinear systems, the fact that the inherent time-scales of the unfolding phenomena are not well separated, is brought into focus. Recent results related to this interdependence, which is one of the most characteristic aspects of complexity and a major challenge in prediction, error estimates and monitoring of nonlinear complex systems, are discussed.

scholarly journals SYMBOL-TO-SYMBOL CORRELATION FUNCTION AT THE FEIGENBAUM POINT OF THE LOGISTIC MAP

2013 ◽  
Vol 23 (07) ◽  
pp. 1350118 ◽  
Author(s):  
K. KARAMANOS ◽  
I. S. MISTAKIDIS ◽  
S. I. MISTAKIDIS
Keyword(s):  
Correlation Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Correlation Functions ◽  
Symbolic Dynamics ◽  
Numerical Experiments ◽  
Statistical Physics ◽  
Logistic Map ◽  
Algorithmic Structure ◽  
Significant Attention

Recently, simple dynamical systems such as the 1-d maps on the interval, gained significant attention in the context of statistical physics and complex systems. The decay of correlations in these systems, can be characterized and measured by correlation functions. In the context of symbolic dynamics of the nonchaotic multifractal attractors (i.e. Feigenbaum attractors), one observable, the symbol-to-symbol correlation function, for the generating partition of the logistic map, is rigorously introduced and checked by numerical experiments. Thanks to the Metropolis–Stein–Stein (MSS) algorithm, this observable can be calculated analytically, giving predictions in absolute accordance with numerical computations. The deep, algorithmic structure of the observable is revealed clearly reflecting the complexity of the multifractal attractor.

scholarly journals Narrativity in Complex Systems

2021 ◽  
pp. 31-50
Author(s):  
Hans U. Fuchs ◽  
Federico Corni ◽  
Elisabeth Dumont
Keyword(s):  
Dynamical Systems ◽  
Complex Systems ◽  
Systems Thinking ◽  
Dynamical Model ◽  
Complex Dynamical Systems ◽  
Natural Complex ◽  
Making Sense ◽  
Heuristic Strategy ◽  
Narrative Understanding

AbstractHumans use narrative for making sense of their environment. In this chapter we ask if, and if so how and to what extent, our narrative mind can help us deal scientifically with complexity. In order to answer this question, and to show what this means for education, we discuss fundamental aspects of narrative understanding of dynamical systems by working on a concrete story. These aspects involve perception of complex systems, experientiality of narrative, decomposition of systems into mechanisms, perception of forces of nature in mechanisms, and the relation of story-worlds to modelling-worlds, particularly in so-called ephemeral mechanisms. In parallel to describing fundamental issues, we develop a practical heuristic strategy for dealing with complex systems in five steps. (1) Systems thinking: Identify phenomena and foreground a system associated with these phenomena. (2) Mechanisms: Find and describe mechanisms responsible for these phenomena. (3) Forces of nature: Learn to perceive forces of nature as agents acting in these mechanisms. (4) Story-worlds and models: Learn how to use stories of forces (of nature) to construct story-worlds; translate the story-worlds into dynamical-model-worlds. (5) Ephemeral mechanisms for one-time, short-lived, unpredictable, and historical (natural) events: Learn how to create and accept ephemeral story-worlds and models. Ephemeral mechanisms and ephemeral story-worlds are a means for dealing with unpredictability inherent in complex dynamical systems. We argue that unpredictability does not fundamentally deny storytelling, modelling, explanation, and understanding of natural complex systems.

Chaos Theory and Complexity Theory

2013 ◽  
Author(s):  
Keith Warren
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Systems Theory ◽  
Complexity Theory ◽  
Chaos Theory ◽  
Mathematical Framework ◽  
Nonlinear Interactions ◽  
Simple Systems ◽  
Over Time

Chaos theory and complexity theory, collectively known as nonlinear dynamics or dynamical systems theory, provide a mathematical framework for thinking about change over time. Chaos theory seeks an understanding of simple systems that may change in a sudden, unexpected, or irregular way. Complexity theory focuses on complex systems involving numerous interacting parts, which often give rise to unexpected order. The framework that encompasses both theories is one of nonlinear interactions between variables that give rise to outcomes that are not easily predictable. This entry provides a nonmathematical introduction, discussion of current research, and references for further reading.

scholarly journals Effective control of complex turbulent dynamical systems through statistical functionals

2017 ◽  
Vol 114 (22) ◽  
pp. 5571-5576 ◽  
Author(s):  
Andrew J. Majda ◽  
Di Qi
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Control Strategy ◽  
Transition To Turbulence ◽  
Effective Control ◽  
Grand Challenge ◽  
Statistical Control ◽  
Energy Principle ◽  
Turbulence Control

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.

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