Complex Systems

2020 ◽  
pp. 209-220
Author(s):  
Stephen K. Reed
Keyword(s):  
Coral Reef ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Computer Science ◽  
Slow Rate ◽  
Earth Science ◽  
Critical Transitions ◽  
Rate Of Recovery ◽  
Over Time ◽  
Sudden Collapse

Dynamical systems are complex systems that fluctuate over time. Sudden transitions occur after reaching a tipping point that can have detrimental consequences, such as the sudden collapse of a coral reef. A slow rate of recovery from smaller challenges can serve as a warning for critical transitions. The increasing importance of complex systems for understanding science requires excellent instruction. NetLogo modules offer one approach for learning about emergent interactions. A review of instruction distinguished between the teaching of complex systems in biology, chemistry, computer science, earth science, ecology, physics, and engineering. Most instruction has focused on the domains of biology and ecology although there is a need to extend coverage to other topics. There is also need for more research on effective teaching because instruction on complex systems is still in its infancy.

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.

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.

scholarly journals Detecting bursty terms in computer science research

2019 ◽  
Vol 122 (1) ◽  
pp. 681-699 ◽  
Author(s):  
E. Tattershall ◽  
G. Nenadic ◽  
R. D. Stevens
Keyword(s):  
Computer Science ◽  
Historical Data ◽  
Science Research ◽  
Detection Algorithm ◽  
Trend Detection ◽  
Free Text ◽  
Research Topics ◽  
Computer Science Research ◽  
Insight Into ◽  
Over Time

AbstractResearch topics rise and fall in popularity over time, some more swiftly than others. The fastest rising topics are typically called bursts; for example “deep learning”, “internet of things” and “big data”. Being able to automatically detect and track bursty terms in the literature could give insight into how scientific thought evolves over time. In this paper, we take a trend detection algorithm from stock market analysis and apply it to over 30 years of computer science research abstracts, treating the prevalence of each term in the dataset like the price of a stock. Unlike previous work in this domain, we use the free text of abstracts and titles, resulting in a finer-grained analysis. We report a list of bursty terms, and then use historical data to build a classifier to predict whether they will rise or fall in popularity in the future, obtaining accuracy in the region of 80%. The proposed methodology can be applied to any time-ordered collection of text to yield past and present bursty terms and predict their probable fate.

scholarly journals On attracting sets in artificial networks: cross activation

2018 ◽  
Vol 16 ◽  
pp. 01005
Author(s):  
Felix Sadyrbaev
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Ordinary Differential Equations ◽  
Critical Points ◽  
Regulatory Networks ◽  
Main Diagonal ◽  
Sigmoidal Function ◽  
Genomic Regulatory Networks ◽  
Over Time

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalues corresponding to any of the critical points are negative. An example for a particular choice of sigmoidal function is considered.

scholarly journals Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chengmei Fan ◽  
M. Mobeen Munir ◽  
Zafar Hussain ◽  
Muhammad Athar ◽  
Jia-Bao Liu
Keyword(s):  
Complex Systems ◽  
Computer Science ◽  
Topological Indices ◽  
Fractal Nature ◽  
Similar Nature ◽  
Zagreb Index ◽  
Recursive Sequences ◽  
And Mathematics

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α , β -Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

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.

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