Nonlinear Dynamics

Edited by Jon Lawhead (University of Southern California, Columbia University)
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  1. Local Lyapunov Exponents Computed From Observed Data.H. D. I. Abarbanel - 1992 - Journal of Nonlinear Science 2 (3):343-365.
    We develop methods for determining local Lyapunov exponents from observations of a scalar data set. Using average mutual information and the method of false neighbors, we reconstruct a multivariate time series, and then use local polynomial neighborhood-to-neighborhood maps to determine the phase space partial derivatives required to compute Lyapunov exponents. In several examples we demonstrate that the methods allow one to accurately reproduce results determined when the dynamics is known beforehand. We present a new recursive QR decomposition method for finding (...)
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  2. We Have Met the Other and We 'Re All Nonlinear: Ethnography as a Nonlinear Dynamic System'.Michael Agar - 2004 - Complexity 10 (2):16-24.
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  3. Nonlinear Dynamics, Mathematical Biology, and Social Science.Philip W. Anderson - 1997 - Complexity 3 (2):50-51.
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  4. 'The Memory of Life Itself': Bénard's Cells and the Cinematography of Self-Organization.David Aubin - 2008 - Studies in History and Philosophy of Science Part A 39 (3):359-369.
    In 1900, the physicist Henri Bénard exhibited the spontaneous formation of cells in a layer of liquid heated from below. Six or seven decades later, drastic reinterpretations of this experiment formed an important component of ‘chaos theory’. This paper therefore is an attempt at writing the history of this experiment, its long neglect and its rediscovery. It examines Bénard’s experiments from three different perspectives. First, his results are viewed in the light of the relation between experimental and mathematical approaches in (...)
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  5. A Cultural History of Catastrophes and Chaos: Around the Institut des Hautes Études Scientifiques.David Aubin - 1998 - Princeton.
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  6. Writing the History of Dynamics Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures.David Aubin & Amy Dalmedico - 2002 - Historia Mathematica 29:1–67.
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  7. How Science Comprehends Chaos.Sunny Auyang - manuscript
    Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of nonlinear (...)
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  8. Nonlinear Dynamics: How Science Comprehends Chaos.Sunny Auyang - manuscript
    Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of nonlinear (...)
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  9. Evaluating Nonlinear Variability of Mental Fatigue Behavioral Indices During Long‐Term Attentive Task.Mahdi Azarnoosh, Ali Motie Nasrabadi, Mohammad Reza Mohammadi & Mohammad Firoozabadi - 2012 - Complexity 17 (6):7-16.
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  10. 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 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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  11. Order Within Chaos.P. Berge, Y. Pomeau & C. Vidal - 1987 - Wiley.
  12. 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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  13. Iterative Learning Control for MIMO Nonlinear Systems with Arbitrary Relative Degree and No States Measurement.Farah Bouakrif - 2014 - Complexity 19 (1):37-45.
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  14. Synergetics and Dynamical Instabilities.G. Caglioti, H. Haken & L. Lugiato (eds.) - 1988 - North Holland.
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  15. Cases, Clusters, Densities: Modeling the Nonlinear Dynamics of Complex Health Trajectories.Brian Castellani, Rajeev Rajaram, Jane Gunn & Frances Griffiths - 2016 - Complexity 21 (S1):160-180.
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  16. On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy.Carlos Castro - 2010 - Foundations of Physics 40 (11):1712-1730.
    A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of (...)
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  17. Clinical Chaos a Therapist's Guide to Nonlinear Dynamics and Therapeutic Change.Linda L. Chamberlain & Michael R. Bütz - 1998
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  18. Workshop on Specific Aspects of Computational Physics and Wavelet Analysis for Modelling Suddenly-Emerging Phenomena in Nonlinear Physics, and Nonlinear Applied Mathematics (PULSES 2006)-.Vincenzo Ciancio, Francesco Farsaci & Antonino Bartolotta - 2006 - In O. Stock & M. Schaerf (eds.), Lecture Notes in Computer Science. Springer Verlag. pp. 3980--821.
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  19. Nonlinear Dynamics in Human Behavior.A. Combs & W. Sulis - 1996
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  20. Analysis of Nonlinear Patterns of Change with Random Coefficient Models.Robert Cudeck & Jeffrey R. Harring - manuscript
    Nonlinear patterns of change arise frequently in the analysis of repeated measures from longitudinal studies in psychology. The main feature of nonlinear development is that change is more rapid in some periods than in others. There generally also are strong individual differences, so although there is a general similarity of patterns for different persons over time, individuals exhibit substantial heterogeneity in their particular response. To describe data of this kind, researchers have extended the random coefficient model to accommodate nonlinear trajectories (...)
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  21. Characterization of Chaos Evident in EEG by Nonlinear Data Analysis.A. Das & P. Das - 2002 - Complexity 7 (3).
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  22. Do Nonlinear Dynamics in Economics Amount to a Kuhnian Paradigm Shift?Mohammed H. I. Dore & J. Barkley Rosser - unknown
    Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...)
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  23. A Bifurcation Model of Neuronal of Spike Train Patterns: A Nonlinear Dynamic Systems Approach.N. H. Farhat, M. Eldefrawy & S. Y. Lin - 1994 - In Karl H. Pribram (ed.), Origins: Brain and Self-Organization. Lawrence Erlbaum. pp. 396.
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  24. Dissipative Many-Body Model and a Nested Operational Architectonics of the Brain.Andrew A. Fingelkurts & Alexander A. Fingelkurts - 2013 - Physics of Life Reviews 10:103-105.
    This paper briefly review a current trend in neuroscience aiming to combine neurophysiological and physical concepts in order to understand the emergence of spatio-temporal patterns within brain activity by which brain constructs knowledge from multiple streams of information. The authors further suggest that the meanings, which subjectively are experienced as thoughts or perceptions can best be described objectively as created and carried by large fields of neural activity within the operational architectonics of brain functioning.
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  25. Nonlinear Dynamics and Intention According to Aquinas.Walter J. Freeman Iii - 2009 - Mind and Matter 6 (2).
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  26. Between Rigor and Reality: Many-Body Models in Condensed Matter Physics.Axel Gelfert - 2015 - In Brigitte Falkenburg & Margaret Morrison (eds.), Why More Is Different: Philosophical Issues in Condensed Matter Physics and Complex Systems. Springer. pp. 201-226.
    The present paper focuses on a particular class of models intended to describe and explain the physical behaviour of systems that consist of a large number of interacting particles. Such many-body models are characterized by a specific Hamiltonian (energy operator) and are frequently employed in condensed matter physics in order to account for such phenomena as magnetism, superconductivity, and other phase transitions. Because of the dual role of many-body models as models of physical sys-tems (with specific physical phenomena as their (...)
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  27. Making Quantum Theory Compatible with Realism.GianCarlo Ghirardi - 2002 - Foundations of Science 7 (1-2):11-47.
    After a brief account of theway quantum theory deals with naturalprocesses, the crucial problem that such atheory meets, the measurement or, better, themacro-objectification problem is discussed.The embarrassing aspects of the occurrence ofentangled states involving macroscopic systemsare analyzed in details. The famous example ofSchroedinger's cat is presented and it ispointed out how the combined interplay of thesuperposition principle and the ensuingentanglement raises some serious difficultiesin working out a satisfactory quantum worldview, agreeing with our definiteperceptions. The orthodox solution to themacro-objectification problem, i.e. (...)
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  28. Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space. [REVIEW]Giancarlo Ghirardi - 1996 - Erkenntnis 45 (2-3):349 - 365.
    Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrödinger's evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea (...)
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  29. Generation of Biological Patterns and Form: Some Physical, Mathematical and Logical Aspects.Alfred Gierer - 1981 - Progress in Biophysics and Molecular Biology 37 (1):1-48.
    While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions are (...)
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  30. A Theory of Biological Pattern Formation.Alfred Gierer & Hans Meinhardt - 1972 - Kybernetik, Continued as Biological Cybernetics 12 (1):30 - 39.
    The paper addresses the formation of striking patterns within originally near-homogenous tissue, the process prototypical for embryology, and represented in particularly purist form by cut sections of hydra regenerating, by internal reorganisation of the pre-existing tissue, a complete animal with head and foot. The essential requirements are autocatalytic, self-enhancing activation, combined with inhibitory or depletion effects of wider range – “lateral inhibition”. Not only de-novo-pattern formation, but also well known, striking features of developmental regulation such as induction, inhibition, and proportion (...)
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  31. Dissipative Quantum Dynamics for Systems Periodic in Time.N. Gisin - 1983 - Foundations of Physics 13 (7):643-654.
    A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The implication (...)
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  32. Dynamical Disease-The Impact of Nonlinear Dynamics and Chaos on Cardiology and Medicine.Leon Glass - 1995 - In R. J. Russell, N. Murphy & A. R. Peacocke (eds.), Chaos and Complexity. Vatican Observatory Publications. pp. 79.
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  33. Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View.Gordon G. Globus - 2005 - Philosophy, Psychiatry, and Psychology 12 (3):229-234.
  34. Important Notes on Lyapunov Exponents.Keying Guan - unknown
    It is shown that the famous Lyapunov exponents cannot be used as the numerical characteristic for distinguishing different kinds of attractors, such as the equilibrium point, the limit closed curve, the stable torus and the strange attractor.
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  35. Catastrophe Models with Nonlinear Regression.Stephen Guastello - 2011 - In Stephen J. Guastello & R. A. M. Gregson (eds.), Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data. Crc Press.
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  36. Nonlinear Evolution of Science.Michal Heller - 1984 - Roczniki Filozoficzne 32 (3):124.
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  37. Nonlinear Dynamical Models as Concrete Construction'.William E. Herfel - 1995 - In HerfelWilliam (ed.), Theories and Models in Scientific Processes. Rodopi. pp. 44--69.
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  38. Nonlinear Response of Chemical Reaction Dynamics.Alfred Hubler & Andrew Friedl - 2014 - Complexity 19 (1):6-8.
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  39. 11/L Nonlinear Dynamics in the Photoreceptor of the Unicellular Alga Euglena Gmcilis: An Application to the Evolutionary Aspects of Consciousness.Ezio M. Insinna - 1998 - In Stuart R. Hameroff, Alfred W. Kaszniak & A. C. Scott (eds.), Toward a Science of Consciousness Ii. MIT Press. pp. 2--407.
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  40. A Nonlinear Integral Transform and a Global Inverse Bifurcation Theory.Yutaka Kamimura - 2011 - Annali della Scuola Normale Superiore di Pisa 10 (4):863-911.
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  41. Extrascientific Uses of Physics: The Case of Nonlinear Dynamics and Legal Theory.Stephen H. Kellert - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S455-.
    This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the (...)
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  42. Extrascientific Uses of Physics: The Case of Nonlinear Dynamics and Legal Theory.Stephen H. Kellert - 2001 - Philosophy of Science 68 (S3):S455-S466.
    This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the (...)
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  43. On Stability of Equilibrium Points in Nonlinear Fractional Differential Equations and Fractional Hamiltonian Systems.Fatemeh Keshtkar, Gholamhussian Erjaee & Mahmoud Boutefnouchet - 2016 - Complexity 21 (2):93-99.
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  44. Heidegger and Cognitive Science.Julian Kiverstein & Michael Wheeler (eds.) - 2012 - Palgrave-Macmillan.
  45. Synergetics and the Images of Future.Helena Knyazeva - 1999 - Futures 31 (3):281-290.
    The hope of finding new methods of predicting the course of historical processes could be connected with the recent developments of the theory of self-organisation, also called synergetics. It provides us with knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general and (...)
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  46. Note on the R2 Measure of Goodness of Fit for Nonlinear Models.Tarald O. Kva°Lseth - 1983 - Bulletin of the Psychonomic Society 21 (1):79-80.
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  47. Beyond Uncertainties: Some Open Questions About Chaos and Ethics.Teresa Kwiatkowska - 2001 - Ethics and the Environment 6 (1):96-115.
    : Lately, a new language for the understanding of the complexity of life (organism, ecosystem, and social system) has been developed. Chaos, fractals, dissipative structures, self-organization, and complex adaptive systems are some of its key concepts. On this view, reality is not the deterministic structure that Newton envisaged, but rather, a partially unknown or at least unpredictable world of multiple possibilities. As the horizon of our knowledge of natural realities expands, the emergent comprehensive perspective requires a radical reconstruction of both (...)
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  48. 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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  49. 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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  50. Theory and Application of Chaos Theory and Family Systems Therapy: A Critical Review of the Literature.Steve B. Lazarre - 2003 - Dissertation, Alliant International University, San Diego
    This paper is an examination of change as an evolving concept progressing from early philosophies to systems theory. The purpose of the paper was to clarify the dimensions of change in the integration of family systems theory and chaos and complexity theory. The key concept in the material change is articulated from selected interdisciplinary sources in the history of ideas, from Parmenides through deep ecology, related to a current integration of family systems and chaos theory. This study examines whether modern (...)
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