Your new post is loading...
Your new post is loading...
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 nonperiodically forced systems. This definition is based on an entropylike 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 wellknown 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 entropybased.
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 firstorder 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 singlevariable 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.
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 bottomheavy at higher biomass. Similar exponents are obtained for community productionbiomass 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 individuallevel scaling, which is not fully understood. These patterns suggest a greater degree of ecosystemlevel organization than previously recognized and a more predictive approach to ecological theory. The predatorprey 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 ;
Via Complexity Digest
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 wellknown artificial neural network, the conditional restricted Boltzmann machine, and define its complexity as the number of hidden units. We conduct experiments with a virtual sixlegged walking creature, which provide evidence for the accuracy of the theoretical predictions.
Human societies use complexity  within their institutions and technologies  to address their various problems, and they need highquality 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 HomerDixon 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=4Vfy3mv57U
Via Complexity Digest
This article explains how to make effective decisions when operating in a complex adaptive system.
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.
Via Claudia Mihai, Complexity Digest, Bill Aukett, Jürgen Kanz
In a new study, physicists reveal how ants cooperate to carry huge chunks of food back to their nests.
Highlights • HANDY is a 4variable thoughtexperiment model for interaction of humans and nature. • The focus is on predicting longterm behavior rather than shortterm forecasting. • Carrying Capacity is developed as a practical measure for forecasting collapses. • A sustainable steady state is shown to be possible in different types of societies. • But overexploitation of either Labor or Nature results in a societal collapse.
Italian New Public Management (NPM) has been mainly characterized by a political orientation toward power decentralization to local governments and privatization of public companies. Nowadays, local utilities in Italy are often run by joint stock companies controlled by public agencies such as Regional and Municipal Administrations. Due to this transformation, these companies must comply with a set of diverse expectations coming from a wide range of stakeholders, related to their financial, competitive and social performance. Such fragmented governance increases the presence of “wicked” problems in the decisionmaking sphere of these entities. Given this multilevel governance structure, how do these agents influence public services performance? In recent years, coordination and interinstitutional joint action have been identified as possible approaches for dealing with governance fragmentation and wicked problems deriving from it. How can we adapt a performance management perspective in order to help us reform the system and so have a better collaboration between the stakeholders involved? In order to address and discuss these research questions, a case study will be developed. The case concerns AMAT, the local utility providing the public transportation service in the Municipality of Palermo (Italy). The result of this study is a dynamic model including a set of performance indicators that help us in understanding the impact of the governing structure on the system’s performance.
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Does the ability to predict the future—perhaps with quantum help—define the fundamental difference between living and inanimate matter?

An introductory conclusion The Systems Approach: principles A few years ago I wrote a blog post about antiplanning as an alternative to the systems approach. Part of the post was devoted to a number of principles of deceptionperception. Churchman discusses their importance in the concluding chapter of The Systems Approach (TSA), which…
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. UNUFLORES developed an interactive platform, the Nexus Tools Platform, for intermodel comparison of existing modeling tools related to WaterSoilWaste Nexus providing detailed model information and advanced filtering based on realtime visualizations.
Amoebas are puny, stupid blobs, so scientists were surprised to learn that they contain 200 times more DNA than Einstein did. Because…
This article explores the concept of the Complex Adaptive Systems and see how this model might apply in various walks of life.
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 realworld 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 technicallyoriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discretetime models, continuoustime models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agentbased 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.
Via Complejidady Economía
Competence in systems thinking is implicitly assumed among the population of engineers and managers — in fact, most technical people claim to be systems ...
Via Ides De Vos, Jürgen Kanz
Photo: Walter Baxter  licensed for reuse CC BYSA 2.0 Brian Castellani (Kent State University) When I attended university in 1984 as a psychology undergraduate in the States, the pathway to...
Via Christophe Bredillet
Historical knowledge is essential to practical applications of ecological economics. Systems of problem solving develop greater complexity and higher costs over long periods. In time such systems either require increasing energy subsidies or they collapse. Diminishing returns to complexity in problem solving limited the abilities of earlier societies to respond sustainably to challenges, and will shape contemporary responses to global change. To confront this dilemma we must understand both the role of energy in sustaining problem solving, and our historical position in systems of increasing complexity.
This paper describes a new concept of cellular automata (CA). XCA consists of a set of arcs (edges). These arcs correspond to cells in CA. At a definite time, the arcs are connected to a directed graph. With each next time step, the arcs are exchanging their neighbors (adjacent arcs) according to rules that are dependent on the status of the adjacent arcs. With the extended cellular automaton (XCA) an artificial world may be simulated starting with a Big Bang. XCA does not require a grid like CA do. However, it can create one, just as the real universe after the big bang generated its own space, which previously did not exist. Examples with different rules show how manifold the concept of XCA is. Like the game of life simulates birth, survival, and death, this game should simulate a system that starts from a singularity, and evolves to a complex space.
The biologist Deborah Gordon has uncovered how ant colonies search efficiently without central organization, an insight that might improve computer networks.
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévywalk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a selfconsistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives. Lévy walks V. Zaburdaev, S. Denisov, and J. Klafter Rev. Mod. Phys. 87, 483 http://dx.doi.org/10.1103/RevModPhys.87.483
Via Complexity Digest
