Complexity & Systems
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Complexity & Systems
Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex.  wikipedia (en)
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The Hidden Power Laws of Ecosystems - Issue 29: Scaling - Nautilus

The Hidden Power Laws of Ecosystems - Issue 29: Scaling - Nautilus | Complexity & Systems | Scoop.it
Here’s how to cause a ruckus: Ask a bunch of naturalists to simplify the world. We usually think in terms of a web of complicated…
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Gary Bamford's curator insight, November 1, 2015 3:52 PM

The complexity of complexity!

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Sequential memory: Binding dynamics

Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories—episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L − 1, where L is the number of modalities.
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[1510.04803] Hidden attractors in fundamental problems and engineering models

[1510.04803] Hidden attractors in fundamental problems and engineering models | Complexity & Systems | Scoop.it
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered.
 
 
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Urban Scaling in Europe

Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using new harmonized definitions for functional urban areas, we examine to what extent these ideas apply to European cities. We show that while most large urban systems in Western Europe (France, Germany, Italy, Spain, UK) approximately agree with theoretical expectations, the small number of cities in each nation and their natural variability preclude drawing strong conclusions. We demonstrate how this problem can be overcome so that cities from different urban systems can be pooled together to construct larger datasets. This leads to a simple statistical procedure to identify urban scaling relations, which then clearly emerge as a property of European cities. We compare the predictions of urban scaling to Zipf's law for the size distribution of cities and show that while the former holds well the latter is a poor descriptor of European cities. We conclude with scenarios for the size and properties of future pan-European megacities and their implications for the economic productivity, technological sophistication and regional inequalities of an integrated European urban system.

 

Urban Scaling in Europe
Luis M. A. Bettencourt, Jose Lobo

http://arxiv.org/abs/1510.00902


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Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University - YouTube

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University - YouTube | Complexity & Systems | Scoop.it

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering." 

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. 

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

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The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

 

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes
Ian A. Hatton, Kevin S. McCann, John M. Fryxell, T. Jonathan Davies, Matteo Smerlak, Anthony R. E. Sinclair, Michel Loreau

Science 4 September 2015:
Vol. 349 no. 6252
http://dx.doi.org/10.1126/science.aac6284 ;


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A Theory of Cheap Control in Embodied Systems

A Theory of Cheap Control in Embodied Systems | Complexity & Systems | Scoop.it
Author Summary Given a body and an environment, what is the brain complexity needed in order to generate a desired set of behaviors? The general understanding is that the physical properties of the body and the environment correlate with the required brain complexity. More precisely, it has been pointed that naturally evolved intelligent systems tend to exploit their embodiment constraints and that this allows them to express complex behaviors with relatively concise brains. Although this principle of parsimonious control has been formulated quite some time ago, only recently one has begun to develop the formalism that is required for making quantitative statements on the sufficient brain complexity given embodiment constraints. In this work we propose a precise mathematical approach that links the physical and behavioral constraints of an agent to the required controller complexity. As controller architecture we choose a well-known artificial neural network, the conditional restricted Boltzmann machine, and define its complexity as the number of hidden units. We conduct experiments with a virtual six-legged walking creature, which provide evidence for the accuracy of the theoretical predictions.
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Civilization Far From Equilibrium - Energy, Complexity, and Human Survival

Human societies use complexity -- within their institutions and technologies -- to address their various problems, and they need high-quality energy to create and sustain this complexity. But now greater complexity is producing diminishing returns in wellbeing, while the energetic cost of key sources of energy is rising fast. Simultaneously, humankind's problems are becoming vastly harder, which requires societies to deliver yet more complexity and thus consume yet more energy. Resolving this paradox is the central challenge of the 21st century. Thomas Homer-Dixon holds the CIGI Chair of Global Systems at the Balsillie School of International Affairs in Waterloo, Canada, and is a Professor at the University of Waterloo.

 

https://www.youtube.com/watch?v=4Vf-y3mv57U


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Making Decisions in a Complex Adaptive System

Making Decisions in a Complex Adaptive System | Complexity & Systems | Scoop.it
This article explains how to make effective decisions when operating in a complex adaptive system.
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Using Chaos Theory to Predict and Prevent Catastrophic 'Dragon King' Events

Using Chaos Theory to Predict and Prevent Catastrophic 'Dragon King' Events | Complexity & Systems | Scoop.it

Stop a stock trade and avoid a catastrophic global financial crash. Seal a microscopic crack and prevent a rocket explosion. Push a button to avert a citywide blackout.

Though such situations are mostly fantasies, a new analysis suggests that certain types of extreme events occurring in complex systems – known as dragon king events – can be predicted and prevented.


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Ali Anani's curator insight, November 9, 2013 3:54 AM

Can we control  the uncontrollable? 

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'Leaders and lifters' help ants move massive meals - BBC News

'Leaders and lifters' help ants move massive meals - BBC News | Complexity & Systems | Scoop.it
In a new study, physicists reveal how ants co-operate to carry huge chunks of food back to their nests.
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FOCUS: Complexity and the failure of quantitative social science

FOCUS: Complexity and the failure of quantitative social science | Complexity & Systems | Scoop.it
Photo: Walter Baxter - licensed for reuse CC BY-SA 2.0 Brian Castellani (Kent State University)   When I attended university in 1984 as a psychology undergraduate in the States, the pathway to...

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Christophe Bredillet's curator insight, July 26, 2015 11:21 AM

I love this map (this one and previous versions) and use(d) it quite often

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Unpredictability and Complexity

Unpredictability and Complexity | Complexity & Systems | Scoop.it

Chaos Theory Applied to the Literary Arts


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Tip Ghosh's curator insight, March 20, 3:08 PM

Visual Side of Complexity

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New guide to systems thinking | From Poverty to Power

New guide to systems thinking | From Poverty to Power | Complexity & Systems | Scoop.it
Systems thinking is fascinating, but often baffling and it's hard to apply it in a practically useful way. A new Oxfam guide tries to help

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Modeling Environmental Complexity | Earth, Atmospheric, and Planetary Sciences | MIT OpenCourseWare

Modeling Environmental Complexity | Earth, Atmospheric, and Planetary Sciences | MIT OpenCourseWare | Complexity & Systems | Scoop.it
This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability—i.e., complexity. Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, we learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Students also learn how to construct minimal mathematical, physical, and computational models that provide informative answers to precise questions. This course is appropriate for advanced undergraduates. Beginning graduate students are encouraged to register for 12.586 (graduate version of 12.086). Students taking the graduate version complete different assignments.
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Chaos Theory in Ecology Predicts Future Populations | Quanta Magazine

Chaos Theory in Ecology Predicts Future Populations | Quanta Magazine | Complexity & Systems | Scoop.it
Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations.
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Sociology and Complexity Science blog: New 2015 Version of Map of the Complexity Sciences

Sociology and Complexity Science blog: New 2015 Version of Map of the Complexity Sciences | Complexity & Systems | Scoop.it
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Principles of deception-perception | CSL4D

Principles of deception-perception | CSL4D | Complexity & Systems | Scoop.it
An introductory conclusion The Systems Approach: principles        A few years ago I wrote a blog post about anti-planning as an alternative to the systems approach. Part of the post was devoted to a number of principles of deception-perception. Churchman discusses their importance in the concluding chapter of The Systems Approach (TSA), which…
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Modelling Tools for Dealing with Environmental Complexity

Modelling Tools for Dealing with Environmental Complexity | Complexity & Systems | Scoop.it
The nexus concept aims at extending ‘integrated management thinking’, which has been applied with varying success in diverse disciplines and has become especially popular in water resources management. UNU-FLORES developed an interactive platform, the Nexus Tools Platform, for inter-model comparison of existing modeling tools related to Water-Soil-Waste Nexus providing detailed model information and advanced filtering based on real-time visualizations.
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Evolution, You’re Drunk - Issue 9: Time - Nautilus

Evolution, You’re Drunk - Issue 9: Time - Nautilus | Complexity & Systems | Scoop.it
Amoebas are puny, stupid blobs, so scientists were surprised to learn that they contain 200 times more DNA than Einstein did. Because…
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Complex Adaptive Systems

Complex Adaptive Systems | Complexity & Systems | Scoop.it
This article explores the concept of the Complex Adaptive Systems and see how this model might apply in various walks of life.
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David Poveda's curator insight, August 27, 2015 1:20 PM

Supply chains are Complex Adaptive Systems. In order to manage them well, this basic fact must be recognized. And they are certainly not well managed with forecasts and ERP´s.

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Introduction to the Modeling and Analysis of Complex Systems | Open SUNY Textbooks

Introduction to the Modeling and Analysis of Complex Systems | Open SUNY Textbooks | Complexity & Systems | Scoop.it

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.


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Why Systems Thinking is Not a Natural Act

Competence in systems thinking is implicitly assumed among the population of engineers and managers — in fact, most technical people claim to be systems ...


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Defining chaos

Defining chaos | Complexity & Systems | Scoop.it
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call “expansion entropy,” and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
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