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
Related categories

323 found
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  1. added 2018-02-14
    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 (...)
  2. added 2017-12-13
    What Are the New Implications of Chaos for Unpredictability?Charlotte Werndl - 2009 - British Journal for the Philosophy of Science 60 (1):195-220.
    From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the (...)
  3. added 2017-12-08
    Harvesting Wave Energy with Resonant Observers.Alfred Hubler & Thomas Kirsh - 2015 - Complexity 20 (4):6-7.
  4. added 2017-09-14
    Limits of Scientific Knowledge.John R. Albright - 2008 - In Paul David Numrich (ed.), The Boundaries of Knowledge in Buddhism, Christianity, and Science. Vandenhoeck & Ruprecht. pp. 15--184.
  5. added 2017-06-07
    The Theory of Chaos. [REVIEW]Steven James Bartlett - 1988 - Methodology and Science: Interdisciplinary Journal for the Empirical Study of the Foundations of Science and Their Methodology 21 (4):300-303.
    A review of James Glieck's _Chaos: Making a New Science_, noting how nonmonotonic functions self-referentially take on their own values and lead to complexity without randomness.
  6. added 2017-02-13
    Parameters Estimation, Mixed Synchronization, and Antisynchronization in Chaotic Systems.Chunni Wang, Yujun He, Jun Ma & Long Huang - 2014 - Complexity 20 (1):64-73.
  7. added 2017-02-13
    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.
  8. added 2017-02-13
    Chaotic or Random? Limits of the Characterization.M. Dubois - 1995 - In R. J. Russell, N. Murphy & A. R. Peacocke (eds.), Chaos and Complexity. Vatican Observatory Publications. pp. 3.
  9. added 2017-02-11
    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.
  10. added 2017-02-11
    A Noise Induced Phase Transition to Chaos in Systems with Static Friction.Alfred Hubler - 2013 - Complexity 18 (1):7-9.
  11. added 2017-02-11
    How to Create a Large Response From Chaotic Systems: Optimal Forcing Functions Complement the Natural Dynamics of a System.Alfred W. Hübler & Glenn C. Foster - 2006 - Complexity 11 (4):11-13.
  12. added 2017-02-08
    Chaotic Hysteresis and Systemic Economic Transformation: Soviet Investment Patterns.J. Barkley Rosser & Robert W. Bond - unknown
    Economies making a transition from centrally planned socialism to market capitalism can experience chaotic hysteresis. This can arise from elements of the previous system persisting even as institutions are transformed with the system possibly experiencing chaos during this conflict. A model of investment cycles accompanied by technological stagnation shows this phenomenon which can be viewed from a cusp catastrophe perspective. Empirical tests of Soviet investment and construction data provide incomplete support for the cusp structure with chaos. Nonlinear structures are found (...)
  13. added 2017-02-08
    Determinism, Predictability and Chaos.G. M. K. Hunt - 1987 - Analysis 47 (3):129 - 133.
  14. added 2017-02-08
    Deterministic Systems.Ryszard Wójcicki - 1975 - Erkenntnis 9 (2):219 - 227.
  15. added 2017-02-07
    Chaotic Attractors in the Therapeutic System.Sandy Berchulskl, Michael Conforti, Irene Guiter-Mazer & Jane Malone - 1995 - World Futures 44 (2):101-113.
  16. added 2017-02-06
    Reviews of the Reviews.Bruce Abell, L. M. Simmons, Michael McMaster & Thomas Petzinger - 1999 - Emergence: Complexity and Organization 1 (2):201-206.
  17. added 2017-02-02
    Kinds of Unpredictability in Deterministic Systems.Gerhard Schurz - 1995 - In P. Weingartner & G. Schurz (eds.), Law and Prediction in the Light of Chaos Research. Springer. pp. 123--41.
  18. added 2017-02-01
    Self-Fulfilling Chaotic Mistakes: Some Examples and Implications.Barkley Rosser - manuscript
    In talks given early in the 1990s, Jean-Michel Grandmont (1998) introduced the concept of the self-fulfilling mistake. This phenomenon can emerge when economic agents cannot distinguish between randomness and determinism, a situation that can occur when the underlying true dynamics are chaotic (Radunskaya, 1994), although such a situation could arise with other forms of complex nonlinear dynamics besides those involving chaotic dynamics. In such a situation, agents may be unable to discern the true dynamics and may adopt simple, boundedly rational (...)
  19. added 2017-01-31
    Review of C. S. Bertuglia and F. Vaio, "Nonlinearity, Chaos, and Complexity".Michael Strevens - 2009 - British Journal for the Philosophy of Science 60 (2):447-451.
  20. added 2017-01-30
    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.
  21. added 2017-01-29
    Comparing Chaos and Complexity : The Quest for Knowledge.Sylvia Elizabeth Greybe - unknown
    Thesis --University of Stellenbosch, 2004.
  22. added 2017-01-29
    Chaos And Grace.David Flagel - 2007 - Journal of Ethics in Mental Health 2:1-1.
  23. added 2017-01-29
    Cosmos or Chaos: Theodicy, Love, and Existential Choice.Royce P. Grubic - 2004 - Dissertation, University of Southern California
    "Cosmos or Chaos: Theodicy, Love, and Existential Choice," explores in detail the social-psychological dimensions of cosmology and the tension between the ideas of cosmos and chaos in the history of Western thought, as these are manifested in philosophy, science, "pure" reason, and religion. In the process, the author seeks to provide the foundation for a viable existentialist social ethic, drawing upon the works of Camus, Sartre, Bergson, Unamuno, Dostoevsky, and the teachings of Theravada Buddhism. ;The dissertation is divided into six (...)
  24. added 2017-01-29
    Order and Chaos in Gregory of Nyssa.Jonathan C. R. Hill - 1999
  25. added 2017-01-29
    The Psychological Meaning of Chaos Translating Theory Into Practice.Frank Masterpasqua & Phyllis A. Perna - 1997
  26. added 2017-01-29
    Tao of Chaos Merging East and West.Katya Mccall Walter - 1994
  27. added 2017-01-29
    Randomness & Undecidability in Physics.Karl Svozil - 1993
  28. added 2017-01-29
    FARJOUN, EMMANUEL and MACHOVER, MOSHE.: "Laws of Chaos". [REVIEW]D. G. Champernowne - 1985 - British Journal for the Philosophy of Science 36:348.
  29. added 2017-01-29
    Brownell's The Philosopher in Chaos: An Attempt to Make Head and Tail of the Modern World. [REVIEW]Cerf Cerf - 1942 - Philosophy and Phenomenological Research 3:495.
  30. added 2017-01-28
    Facing Up to the Real: Chaos, Fantasy and Work: About Hans Blumenberg.Sebastián Alejandro González Montero - 2008 - Universitas Philosophica 25 (51).
    Three main features of the mythos and logos relationship will be examined in this article; beginning with the symbolic elaboration fantasy binds chaos and how beings/forces of the universe are classified by it. A second concern studies two strategies of thought to face chaos: one, unfolding the mythical assumption of a beings /powers distribution filling the universe forever and, another, based on a metaphysical supposition of the existence of 'something' eternal and infinite from which everything stems. It is about dogma (...)
  31. added 2017-01-28
    Julian Barnes’s ‘Shipwreck’ or Recycling Chaos Into Art.TomÁs Monterrey - 2004 - Clio: A Journal of Literature, History, and the Philosophy of History 33 (4):415-426.
  32. added 2017-01-28
    Chaos and Reliable Knowledge.Maralee Harrell - 2000 - Dissertation, University of California, San Diego
    Most of the recent work in chaos theory has been the development of data analysis tools for analyzing chaotic data. It is based upon the results of the application of these tools that many researchers have made claims that such phenomena as heartbeats, planetary orbits, and chemical reactions are chaotic. ;The first part of my dissertation is concerned with investigating the standard methods that are used to determine whether a system is chaotic, and the requirements of these methods. I begin (...)
  33. added 2017-01-28
    Laws of Chaos.Emmanuel Farjoun & Moshe Machover - 1985 - British Journal for the Philosophy of Science 36 (3):348-352.
  34. added 2017-01-28
    Robert B. Carroll: "From Chaos to Covenant". [REVIEW]Howard N. Bream - 1985 - The Thomist 49 (1):154.
  35. added 2017-01-28
    The Philosopher in Chaos: An Attempt to Make Head and Tail of the Modern World.Baker Brownell - 1943 - Philosophy and Phenomenological Research 3 (4):495-499.
  36. added 2017-01-28
    W. G. Peck, From Chaos to Catholicism. [REVIEW]J. C. Mantripp - 1920 - Hibbert Journal 19:177.
  37. added 2017-01-27
    Harmony or Chaos.Dr Klaus Vella Bardon - 2013 - The Chesterton Review 39 (3/4):215-217.
  38. added 2017-01-27
    Borrowed Knowledge: Chaos Theory and the Challenge of Learning Across Disciplines.Stephen H. Kellert - 2008 - University of Chicago Press.
    What happens to scientific knowledge when researchers outside the natural sciences bring elements of the latest trend across disciplinary boundaries for their own purposes? Researchers in fields from anthropology to family therapy and traffic planning employ the concepts, methods, and results of chaos theory to harness the disciplinary prestige of the natural sciences, to motivate methodological change or conceptual reorganization within their home discipline, and to justify public policies and aesthetic judgments. Using the recent explosion in the use of chaos (...)
  39. added 2017-01-27
    Clinical Chaos a Therapist's Guide to Nonlinear Dynamics and Therapeutic Change.Linda L. Chamberlain & Michael R. Bütz - 1998
  40. added 2017-01-27
    Application of Chaos Theory to Psychological Models.Rae Fortunato Blackerby - 1998
    This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. ;Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the (...)
  41. added 2017-01-27
    Chaos and the Evolving Ecological Universe.Sally J. Goerner - 1995
  42. added 2017-01-27
    Order and Chaos in Nature and Society. Chaos and Music.Rainer Hegselmann - 1993 - Vienna Circle Institute Yearbook 1:296-298.
    Chaos, order and the transitions between them — these are issues which are being intensively debated in many different sciences at present. These debates are by no means restricted to the natural sciences. Numerous popularizations confirm the existence of a broad following which is intensely interested in the phenomenon. This provided the background against which the Institute Vienna Circle organized a symposion, as international as it was interdisciplinary, entitled “Order and Chaos in Nature and Society”, held on 18 – 21 (...)
  43. added 2017-01-27
    Universality in Chaos a Reprint Selection.C. Predrag Cvitanovi - 1984
  44. added 2017-01-26
    Chaos, Creativity and Self-Renewal.A. Montouri - forthcoming - World Futures. The Journal of General Evolution.
  45. added 2017-01-26
    Children's Ideas About the Solar System and the Chaos in Learning Science.John G. Sharp & Paul Kuerbis - 2006 - Science Education 90 (1):124-147.
  46. added 2017-01-26
    Causality in Chaotic Environment: Does Strong Causality Break Down in Deterministic Chaos?Max Urchs - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 89:187.
  47. added 2017-01-26
    The Nature of Scientific Revolutions From the Vantage Point of Chaos Theory.Rocco J. Perla & James Carifio - 2005 - Science & Education 14 (3-5):263-290.
  48. added 2017-01-26
    Chaos and Complexity: New Practices for an Emergent Concept of Family Health in a Brazilian Experience.Ivan A. Guerrini & Regina Stella Spagnuolo - 2004 - Emergence: Complexity and Organization 6 (4).
  49. added 2017-01-26
    Review: Chaos of Disciplines (Review). [REVIEW]Ali Bulent Cambel - 2004 - Perspectives in Biology and Medicine 47 (2):303-304.
  50. added 2017-01-26
    Marian Smoluchowski-A Forerunner of the Chaos Theory.Wladyslaw Krajewski - 2001 - Poznan Studies in the Philosophy of the Sciences and the Humanities 74:185-188.
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