Chaos

Edited by Jon Lawhead (University of Southern California)
About this topic
Summary Chaotic systems have two definitive properties: (1) they are deterministic, and (2) their long-term behavior sensitively depends on their initial conditions.  Edward Lorenz, the father of modern chaos theory, summarized chaos as being present when "the past determines the future, but the approximate past doesn't determine the approximate future."  The most familiar depiction of chaotic behavior is the so-called "butterfly effect," in which a very small perturbation of the global weather system (the flapping of a butterfly's wings in Argentina) results in a very large change to that same system (the genesis of a hurricane in Texas three weeks later).  Of course, it is clear that not all butterfly flaps spawn hurricanes (thankfully!), so the central problem of chaos theory is the precise mathematical modeling of this sensitive dependence relationship, and the determination of when very small changes are likely to have very large effects.  Many important natural systems exhibit chaotic dynamics under certain circumstances; in addition to the global weather system, the global climate, social systems (like the economy), and biological systems (like the human brain) can sometimes exhibit chaotic dynamics.  The understanding and modeling of chaos is an important part of understanding complex natural systems.
Key works Lorenz 1963 is the earliest mature articulation of the central ideas of chaos theory, though it builds on concepts from Saltzman 1962.  More recent developments of the formalism include Abarbanel 1992 and Guan unknown.  The concept has also been expanded to define a notion of structural chaos by Mayo-Wilson 2015.
Introductions Strogatz 2001Auyang manuscriptLorenz 1963Lawhead forthcoming
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  1. Universal Complexity in Action: Active Condensed Matter, Integral Medicine, Causal Economics and Sustainable Governance.Andrei P. Kirilyuk - manuscript
    We review the recently proposed universal concept of dynamic complexity and its new mathematics based on the unreduced interaction problem solution. We then consider its progress-bringing applications at various levels of complex world dynamics, including complex-dynamical nanometal physics and living condensed matter, unreduced nanobiosystem dynamics and the integral medicine concept, causally complete management of complex economical and social dynamics, and the ensuing concept of truly sustainable world governance.
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  2. Order Out of Chaos. [REVIEW]Kent Johnson - unknown - Eidos: The Canadian Graduate Journal of Philosophy 3.
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  3. The Rise of the Technobionts: Toward a New Ontology to Understand Current Planetary Crisis.Gustavo Magallanes Guijón & O. López-Corona - forthcoming - Researchers.One.
    Inhere we expand the concept of Holobiont to incorporate niche construction theory in order to increase our understanding of the current planetary crisis. By this, we propose a new ontology, the Ecobiont, as the basic evolutionary unit of analysis. We make the case of Homo Sapiens organized around modern cities (technobionts) as a different Ecobiont from classical Homo Sapiens (i.e. Hunter- gatherers Homo Sapiens). We consider that Ecobiont ontology helps to make visible the coupling of Homo Sapiens with other biological (...)
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  4. Structural Modeling Error and the System Individuation Problem.Jon Lawhead - forthcoming - British Journal for the Philosophy of Science.
    Recent work by Frigg et. al. and Mayo-Wilson have called attention to a particular sort of error associated with attempts to model certain complex systems: structural modeling error. The assessment of the degree of SME in a model presupposes agreement between modelers about the best way to individuate natural systems, an agreement which can be more problematic than it appears. This problem, which we dub “the system individuation problem” arises in many of the same contexts as SME, and the two (...)
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  5. Chaos, Creativity and Self-Renewal.A. Montouri - forthcoming - World Futures. The Journal of General Evolution.
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  6. Creative Undecidability of Real-World Dynamics and the Emergent Time Hierarchy.Andrei P. Kirilyuk - 2020 - FQXi Essay Contest 2019-2020 “Undecidability, Uncomputability, and Unpredictability”.
    The unreduced solution to the arbitrary interaction problem, absent in the standard theory framework, reveals many equally real and mutually incompatible system configurations, or "realizations". This is the essence of universal dynamic undecidability, or multivaluedness, and the ensuing causal randomness (unpredictability), non-computability, irreversible time flow (evolution, emergence), and dynamic complexity of every real system, object, or process. This creative undecidability of real-world dynamics provides causal explanations for "quantum mysteries", relativity postulates, cosmological problems, and the huge efficiency of high-complexity phenomena, such (...)
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  7. Panpsichismo, teoria della complessità e proprietà quanto-psicoidi del Sè.Donato Santarcangelo - 2020 - Ombra 13.
    The thesis of this paper is that panpsychism theory is very close to jungian theory, especially thinking of the quantum psychoid aspects of C.G.Jung and W.Pauli theory: a psyche that touches matter and matter with a “latent psyche”. The two theories seem to describe the same reality, an animation of matter in a spiritual sense, as the jungian Self seems to do at a higher level.The complexity theory appears instead to be a description of reality still nomothetic.
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  8. De amore.Andrej Poleev - 2018
  9. Theory of Everything, Ultimate Reality and the End of Humanity: Extended Sustainability by the Universal Science of Complexity.Andrei P. Kirilyuk - 2017 - Beau Bassin: LAP LAMBERT Academic Publishing.
    Instead of postulated fixed structures and abstract principles of usual positivistic science, the unreduced diversity of living world reality is consistently derived as dynamically emerging results of unreduced interaction process development, starting from its simplest configuration of two coupled homogeneous protofields. The dynamically multivalued, or complex and intrinsically chaotic, nature of these real interaction results extends dramatically the artificially reduced, dynamically single-valued projection of standard theory and solves its stagnating old and accumulating new problems, “mysteries” and “paradoxes” within the unified (...)
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  10. Complex-Dynamic Origin of Quantised Relativity and Its Manifestations at Higher Complexity Levels.Andrei P. Kirilyuk - 2017 - In A. P. Kirilyuk, Theory of Everything, Ultimate Reality and the End of Humanity: Extended Sustainability by the Universal Science of Complexity. Beau Bassin: LAP LAMBERT Academic Publishing. pp. 186-194.
    Unified and causal complex-dynamic origin of standard (special and general) relativistic and quantum effects revealed previously at the lowest levels of world interaction dynamics is explicitly generalised to all higher levels of unreduced interaction processes, thus additionally confirming the causally complete character of complex-dynamical, naturally quantised relativity, which does not contain any artificially added, abstract postulates. We demonstrate some elementary applications of this generalised quantum relativity at higher levels of complex brain and social interaction dynamics.
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  11. Chaos to Complexity: Leveling the Playing Field for Measuring Value in Primary Care.William P. Moran, Jingwen Zhang, Mulugeta Gebregziabher, Elisha L. Brownfield, Kimberly S. Davis, Andrew D. Schreiner, Brent M. Egan, Raymond S. Greenberg, T. Rogers Kyle, Justin E. Marsden, Sarah J. Ball & Patrick D. Mauldin - 2017 - Journal of Evaluation in Clinical Practice 23 (2):430-438.
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  12. A Philosophical Analysis of Chaos Theory.Lena Zuchowski - 2017 - Cham: Palgrave MacMillan.
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  13. Global Chaos Synchronization of New Chaotic System Using Linear Active Control.Israr Ahmad, Azizan Bin Saaban, Adyda Binti Ibrahim & Mohammad Shahzad - 2016 - Complexity 21 (1):379-386.
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  14. Chaos and Stochastic Models in Physics: Ontic and Epistemic Aspects.Sergio Caprara & Angelo Vulpiani - 2016 - In Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science. Springer.
    There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers, it is possible to understand that the two concepts are completely unrelated. In few words we can say that determinism is ontic and has to do with how Nature behaves, while predictability is epistemic and is related to what the human beings are able to compute. An analysis of the Lyapunov exponents and the Kolmogorov-Sinai entropy shows how deterministic chaos, although with an (...)
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  15. Mutual Synchronization Behavior for Chaotic Systems Via Limited Capacity Communication Channels.Xingyuan da LinWang, Fuchen Zhang & Yi Yao - 2016 - Complexity 21 (6):335-342.
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  16. More Than 20 Years of Chaos in Economics.Marisa Faggini & Anna Parziale - 2016 - Mind and Society 15 (1):53-69.
    Starting for the good results reached in physics researchers in economics and finance have been interested in testing nonlinear dependence and chaos in economic models and data. A wide variety of reasons for this interest have been suggested, including an attempt to improve the forecasting accuracy of linear time series models and to better explain the dynamics of the underlying variables of interest using a richer class of models than that permitted by limiting the set to the linear case. But (...)
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  17. 3. Chaos and Ethics.Raymond Geuss - 2016 - In Reality and its Dreams. Harvard University Press. pp. 51-63.
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  18. The Control of Chaotic Systems with Unknown Parameters and External Disturbance Via Backstepping-Like Scheme.Runzi Luo & Yanhui Zeng - 2016 - Complexity 21 (S1):573-583.
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  19. Chaos Imagined: Literature, Art, Science.Martin Meisel - 2016 - Cambridge University Press.
    The stories we tell in our attempt to make sense of the world, our myths and religion, literature and philosophy, science and art, are the comforting vehicles we use to transmit ideas of order. But beneath the quest for order lies the uneasy dread of fundamental disorder. True chaos is hard to imagine and even harder to represent, especially without some recourse to the familiar coherency of order. In this book, Martin Meisel considers the long effort to conjure, depict, and (...)
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  20. Finite-Time Stabilization of a Class of Chaotic Systems with Matched and Unmatched Uncertainties: An LMI Approach.Saleh Mobayen - 2016 - Complexity 21 (5):14-19.
    This study presents the fundamental concepts and technical details of a U-model-based control system design framework, including U-model realisation from classic model sets, control system design procedures, and simulated showcase examples. Consequently, the framework provides readers with clear understandings and practical skills for further research expansion and applications. In contrast to the classic model-based design and model-free design methodologies, this model-independent design takes two parallel formations: it designs an invariant virtual controller with a specified closed-loop transfer function in a feedback (...)
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  21. Chaos Control of Uncertain Time-Delay Chaotic Systems with Input Dead-Zone Nonlinearity.Ming-Chang Pai - 2016 - Complexity 21 (3):13-20.
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  22. Determinism.Charlotte Werndl - 2016 - In Meghan Griffith, Kevin Timpe & Neil Levy (eds.), Routledge Companion to Free Will. Routledge.
    This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.
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  23. Qualitative Behavior of the Lorenz-Like Chaotic System Describing the Flow Between Two Concentric Rotating Spheres.Fuchen Zhang, Xiaofeng Liao & Guangyun Zhang - 2016 - Complexity 21 (S2):67-72.
    In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also obtained (...)
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  24. Dynamics of Two Classes of Lorenz-Type Chaotic Systems.Fuchen Zhang, Chunlai Mu, Guangyun Zhang & Da Lin - 2016 - Complexity 21 (1):363-369.
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  25. Chaos.Robert Bishop - 2015 - Stanford Encyclopedia of Philosophy.
    The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...)
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  26. Harvesting Wave Energy with Resonant Observers.Alfred Hubler & Thomas Kirsh - 2015 - Complexity 20 (4):6-7.
  27. “Das Andere der Natur” - Eine Abhandlung über das gleichnamige Buch von JC Schmidt im Hirzel-Verlag. [REVIEW]Paul Gottlob Layer - 2015 - Universitas, Heidelberg 70 (830):62-73.
    Nicht Stabilität, sondern Instabilität sei der Grundcharakter der Natur, so hören wir von Jan Schmidt als Auftakt zu seinem Buch „Das Andere der Natur“ (Hirzel-Verlag, 2015). „Das Eine der Natur“, welches reduktionistisch zu erfassen ist, soll durch ein „Anderes“ ergänzt werden. Von dieser anderen Seite her zeigt sich „Natur ... auch (als) instabil, komplex, chaotisch, zufällig, emergent...“, und aus dieser Sicht des Naturgeschehens heraus will der Autor eine Philosophie der Instabilität entwerfen. Der gelernte Physiker und Philosoph lehrt an der Hochschule (...)
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  28. Structural Chaos.Conor Mayo-Wilson - 2015 - Philosophy of Science 82 (5):1236-1247.
    A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...)
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  29. Ultimate Bound Sets of a Hyperchaotic System and its Application in Chaos Synchronization.Hassan Saberi Nik, Sohrab Effati & Jafar Saberi-Nadjafi - 2015 - Complexity 20 (4):30-44.
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  30. What is Chaos and How is It Relevant for Philosophy of Mind?John M. Ostrowick - 2015 - South African Journal of Philosophy 34 (3):323-335.
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  31. Recensione di Michael Strevens' "Bigger than chaos. Understanding complexity through probability". [REVIEW]Aldo Filomeno - 2014 - Aphex 10.
  32. Czas, Starzy I Młodzi, Czyli Chaos Uchwycony.Marta Gibińska - 2014 - Kronos - metafizyka, kultura, religia 3 (30).
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  33. Lightning in a Bottle: Complexity, Chaos, and Computation in Climate Science.Jon Lawhead - 2014 - Dissertation, Columbia University
    Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...)
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  34. Trinity in Relation: Creation, Incarnation, and Grace in an Evolving Cosmos by Gloria L. Schaab. [REVIEW]Marc A. Pugliese - 2014 - Process Studies 43 (1):106-110.
    Book Review of "Trinity in Relation: Creation, Incarnation, and Grace in an Evolving Cosmos" by Gloria L. Schaab.
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  35. Parameters Estimation, Mixed Synchronization, and Antisynchronization in Chaotic Systems.Chunni Wang, Yujun He, Jun Ma & Long Huang - 2014 - Complexity 20 (1):64-73.
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  36. Voltage Transformer Ferroresonance Analysis Using Multiple Scales Method and Chaos Theory.A. Abbasi, S. H. Fathi, G. B. Gharehpatian, A. Gholami & H. R. Abbasi - 2013 - Complexity 18 (6):34-45.
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  37. Chaos Beyond Order: Overcoming the Quest for Certainty and Conservation in Modern Western Sciences.Riccardo Baldissone - 2013 - Cosmos and History 9 (1):35-49.
    Chaos theory not only stretched the concept of chaos well beyond its traditional semantic boundaries, but it also challenged fundamental tenets of physics and science in general. Hence, its present and potential impact on the Western worldview cannot be underestimated. I will illustrate the relevance of chaos theory in regard to modern Western thought by tracing the concept of order, which modern thinkers emphasised as chaos’ dichotomic counterpart. In particular, I will underline how the concern of seventeenth-century natural philosophers with (...)
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  38. Harmony or Chaos.Dr Klaus Vella Bardon - 2013 - The Chesterton Review 39 (3/4):215-217.
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  39. Harmony or Chaos.Klaus Vella Bardon - 2013 - The Chesterton Review 39 (3/4):215-217.
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  40. On Two Mathematical Definitions of Observational Equivalence: Manifest Isomorphism and Epsilon-Congruence Reconsidered.Christopher Belanger - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (2):69-76.
    In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...)
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  41. My Life in Chaos.Allan Leslie Combs - 2013 - World Futures 69 (4-6):248 - 268.
    (2013). My Life in Chaos. World Futures: Vol. 69, The Complexity of Life and Lives of Complexity, pp. 248-268.
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  42. A Noise Induced Phase Transition to Chaos in Systems with Static Friction.Alfred Hubler - 2013 - Complexity 18 (1):7-9.
  43. Synchronization of Circular Restricted Three Body Problem with Lorenz Hyper Chaotic System Using a Robust Adaptive Sliding Mode Controller.Ayub Khan & Mohammad Shahzad - 2013 - Complexity 18 (6):58-64.
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  44. Arystoteles i chaos prekosmiczny (De cael. 3.2, 301a11-20).Maria Marcinkowska-Rosół - 2013 - Diametros 35:65-83.
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  45. Scientific Uncertainty: A User's Guide.Seamus Bradley - 2012 - Grantham Institute on Climate Change Discussion Paper.
    There are different kinds of uncertainty. I outline some of the various ways that uncertainty enters science, focusing on uncertainty in climate science and weather prediction. I then show how we cope with some of these sources of error through sophisticated modelling techniques. I show how we maintain confidence in the face of error.
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  46. Chaos E Ade in Hes. Th. 720-819.Michela Lombardi - 2012 - Hermes 140 (1):1-24.
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  47. Philosophical Reflexion on Chaos Theory.Lukas Zamecnik - 2012 - Filosoficky Casopis 60 (5).
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  48. Vision of Oneness.Ignazio Licata & Ammar J. Sakaji (eds.) - 2011 - Aracne Editrice.
    A cura di Ignazio Licata, Ammar J. Sakaji Jeffrey A. Barrett, Enrico Celeghini, Leonardo Chiatti, Maurizio Consoli, Davide Fiscaletti, Ervin Goldfain, Annick Lesne, Maria Paola Lombardo, Mohammad Mehrafarin, Ronald Mirman, Ulrich Mohrhoff, Renato Nobili, Farrin Payandeh, Eliano Pessa, L.I Petrova, Erasmo Recami, Giovanni Salesi, Francesco Maria Scarpa, Mohammad Vahid Takook, Giuseppe Vitiello This volume comes out from an informal discussion between friends and colleagues on the answer:what topic do you think as fundamental in theoretical physics nowadays? Obviously wereceived different answers (...)
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  49. The Problem of Irreversibility, From Fourier to Chaos Theory.Olimpia Lombardi - 2011 - In Oscar Nudler (ed.), Controversy Spaces: A Model of Scientific and Philosophical Change. John Benjamins.
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  50. Organizing at the Edge of Chaos: Insights From Action Research.Donald MacLean & R. MacIntosh - 2011 - In Peter Allen, Steve Maguire & Bill McKelvey (eds.), The Sage Handbook of Complexity and Management. Sage Publications. pp. 235--253.
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1 — 50 / 338