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Journal articles on the topic 'Chaos and complexity theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Woehle, Ralph. "Complexity Theory, Nonlinear Dynamics, and Change: Augmenting Systems Theory." Advances in Social Work 8, no. 1 (April 30, 2007): 141–51. http://dx.doi.org/10.18060/137.

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Social work change processes are addressed in terms of complexity theory and nonlinear dynamics, adding the edge-of-chaos, as well as chaos to the entropy and homeostasis of ecosystems theory. Complexity theory sees the edge-of-chaos as valuable to living systems.A logistic difference equation is utilized to model the nonlinear dynamics of the hypothetical contentment of an individual. The modeling suggests that substantial input would be required to move an individual from homeostasis to the beneficial stage at the edge-of-chaos, but that too much input might result in chaos.With good measurement and data observed over time, social work might benefit from complexity theory and nonlinear dynamics, which are already advancing in related disciplines.

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2

Johnson, Jonathan L., and Brian K. Burton. "Chaos and Complexity Theory for Management." Journal of Management Inquiry 3, no. 4 (December 1994): 320–28. http://dx.doi.org/10.1177/105649269434005.

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3

Tsoukas, Haridimos. "Introduction: Chaos, Complexity and Organization Theory." Organization 5, no. 3 (August 1998): 291–313. http://dx.doi.org/10.1177/135050849853001.

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4

Érdi, Péter. "Complexity underestimated?" Behavioral and Brain Sciences 26, no. 6 (December 2003): 676–77. http://dx.doi.org/10.1017/s0140525x03310155.

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Instead of commenting directly on Foundations of Language: Brain, Meaning, Grammar, Evolution, I provide some remarks from an interdisciplinary view. Language theory is examined from the perspective of the theory of complex systems. The gestural-vocal dichotomy, network theory, evolutionary mechanisms/algorithms, chaos theory, and constructive approach are briefly mentioned.

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5

Ichinose, Natsuhiro, and Kazuyuki Aihara. "Challange to Complexity. (3). Theory of Chaos." Journal of the Institute of Television Engineers of Japan 50, no. 3 (1996): 358–65. http://dx.doi.org/10.3169/itej1978.50.358.

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6

SENGUPTA, A. "TOWARD A THEORY OF CHAOS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3147–233. http://dx.doi.org/10.1142/s021812740300851x.

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This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space [Sengupta & Ray, 2000] and the topological theory of convergence. Order, chaos and complexity are described as distinct components of this unified mathematical structure that can be viewed as an application of the theory of convergence in topological spaces to increasingly nonlinear mappings, with the boundary between order and complexity in the topology of graphical convergence being the region in (Multi(X)) that is susceptible to chaos. The paper uses results from the discretized spectral approximation in neutron transport theory [Sengupta, 1988, 1995] and concludes that the numerically exact results obtained by this approximation of the Case singular eigenfunction solution is due to the graphical convergence of the Poisson and conjugate Poisson kernels to the Dirac delta and the principal value multifunctions respectively. In (Multi(X)), the continuous spectrum is shown to reduce to a point spectrum, and we introduce a notion of latent chaotic states to interpret superposition over generalized eigenfunctions. Along with these latent states, spectral theory of nonlinear operators is used to conclude that nature supports complexity to attain efficiently a multiplicity of states that otherwise would remain unavailable to it.

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7

MASON, ROGER B. "COPING WITH COMPLEXITY AND TURBULENCE - AN ENTREPRENEURIAL SOLUTION." Journal of Enterprising Culture 14, no. 04 (December 2006): 241–66. http://dx.doi.org/10.1142/s0218495806000155.

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This paper considers the adoption of an entrepreneurial orientation as a paradigm for companies operating in a complex and turbulent environment, viewing the environment as a complex and turbulent system in terms of chaos theory. Approaches suggested by chaos theory are compared with the entrepreneurial orientation to identify if such an orientation matches these suggested approaches. Literature on chaos theory and entrepreneurship is compared, and a short case is presented, providing an illustration of how a company operating successfully in a complex and turbulent environment has used the principles of an entrepreneurial orientation. The paper identifies considerable similarity between the management approaches suggested by chaos theory and the principles of the entrepreneurial orientation, indicating that chaos theory may provide the theoretical underpinning of the relationship between entrepreneurial orientation and turbulent environments. The case also shows how an entrepreneurial orientation has been successfully used in a complex and turbulent environment. The conclusion is that companies operating in a complex and turbulent environment could benefit from adopting an entrepreneurial orientation.

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8

Burke, John P., and Stanley L. Pestotnik. "Antibiotic resistance-systems thinking, chaos and complexity theory." Current Opinion in Infectious Diseases 12, no. 4 (August 1999): 317–19. http://dx.doi.org/10.1097/00001432-199908000-00001.

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9

Warren, K., C. Franklin, and C. L. Streeter. "New Directions in Systems Theory: Chaos and Complexity." Social Work 43, no. 4 (July 1, 1998): 357–72. http://dx.doi.org/10.1093/sw/43.4.357.

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10

Petrovic, Slavica. "The complexity paradigm in management reconceptualizing." Ekonomski anali 50, no. 167 (2005): 107–39. http://dx.doi.org/10.2298/eka0567107p.

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Chaos and complexity theory is a special, functionalist systems approach to dealing with complex, dynamic, nonlinear systems. Through treating organizations as complex, with their environments coevolving, nonlinear systems, complexity theory is aimed at creative research of their erratic nature. When an organization is in a state of bounded instability, at the edge of chaos, order and disorder are intertwined, its behavior is irregular and unpredictable but has some pattern. According to the complexity paradigm organizations have to strive to avoid the equilibrium states of stability and instability. They have instead to strive to remain in a state of bounded instability, at the edge of chaos, where they are able to display their full potential for creativity and innovation.

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11

Филатова, O. Filatova, Еськов, Valeriy Eskov, Хадарцев, Aleksandr Khadartsev, Филатов, and M. Filatov. "Living Systems (Complexity) From the Point of Chaos and Self-Organization Theory." Journal of New Medical Technologies 22, no. 3 (September 15, 2015): 25–32. http://dx.doi.org/10.12737/13294.

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Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.

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12

Kernick, D. "Migraine — New Perspectives from Chaos Theory." Cephalalgia 25, no. 8 (August 2005): 561–66. http://dx.doi.org/10.1111/j.1468-2982.2005.00934.x.

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Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.

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13

Peterson, Mark F., and Mark R. Meckler. "Cuban-American Entrepreneurs: Chance, Complexity and Chaos." Organization Studies 22, no. 1 (January 2001): 31–57. http://dx.doi.org/10.1177/017084060102200102.

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Bouchikhi (1993) introduces themes from chaos and complexity theory to gain an understanding about chance in entrepreneurship. We expand on these themes using an example from the Cuban immigrants to South Florida to increase the dynamism of Waldinger et al.'s (1990) model of immigrant entrepreneurship. These complexity and chaos themes are: (1) large differences in outcomes can come from small differences in initial conditions; (2) largely unpredictable, radical changes can be intermixed with and become directly dependent on incremental, predictable changes; (3) short-term predictability can accompany long-term nonpredictability; (4) seemingly random patterns can show an apparent attraction to specific configurations; and (5), mutual influence among a small number of predictors can appear to be random. An example from among the leading Cuban-born entrepreneurs illustrates three levels of generality in entrepreneurship theory. Most generally, this person's career reflects abstract conclusions about entrepreneurship in the larger community. At a second level, it illustrates the uniqueness in the pattern of entrepreneurship for one sub-group, a specific age cadre. At a third level, it illustrates the uniquenesses of an individual's personal history. Insights at these three levels of generality appear as we follow a systematic, theory-based, case-study method.

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14

Benvenuto, Sergio. "Simplistic Complexity: A Discussion on Psychoanalysis and Chaos Theory." World Futures 61, no. 3 (March 16, 2005): 181–87. http://dx.doi.org/10.1080/02604020590917591.

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15

Cornforth, Amber. "COPD self-management supportive care: chaos and complexity theory." British Journal of Nursing 22, no. 19 (October 2013): 1101–4. http://dx.doi.org/10.12968/bjon.2013.22.19.1101.

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16

Zhou, Xiong. "Computer Network Behavior Research Based on the Theory of Complexity." Applied Mechanics and Materials 556-562 (May 2014): 5822–24. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.5822.

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Guided by the thought of system integrity, complex behavior of computer network is thoroughly study based on complexity theory. Based on chaos theory complex behavior property of computer networks traffic with different time-scale is deeply researched, the result indicates the universe of the chaos and scale-free behavior in real computer networks. The network behavior evolvement model that correctly describes function mechanism of general real networks is presented, and formal description of the evolvement rules is implemented, the fluctuations formula of input traffic is also deducted. Based on the mean field model of network traffic, the dynamical properties of network traffic system is analyzed, and the condition of chaotic dynamical behavior is achieved under mean field hypothesis.

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17

Andersson, Åke E., and Wei-Bin Zhang. "Nonlinearity in social dynamics – order versus chaos." Discrete Dynamics in Nature and Society 1, no. 2 (1997): 111–26. http://dx.doi.org/10.1155/s1026022697000125.

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This paper discusses the significance of applying nonlinear theory to examine the complexity of social and economic evolution. First, we generally examine possible implications of nonlinear theory for analyzing the complexity of human societies. Second, we select two socio-economic models to illustrate our viewpoints.

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18

Rosnay, Joël de. "Symbionomic Evolution: From Complexity and Systems Theory, to Chaos Theory and Coevolution." World Futures 67, no. 4-5 (May 2011): 304–15. http://dx.doi.org/10.1080/02604027.2011.585896.

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19

Barnett, William A., Apostolos Serletis, and Demitre Serletis. "NONLINEAR AND COMPLEX DYNAMICS IN ECONOMICS." Macroeconomic Dynamics 19, no. 8 (November 7, 2014): 1749–79. http://dx.doi.org/10.1017/s1365100514000091.

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This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

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20

Lima Júnior, Ronaldo Mangueira. "Complexity in second language phonology acquisition." Revista Brasileira de Linguística Aplicada 13, no. 2 (June 11, 2013): 549–76. http://dx.doi.org/10.1590/s1984-63982013005000006.

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This paper aims at situating the representation and investigation of second language phonology acquisition in light of complexity theory. The first section presents a brief historical panorama of complexity and chaos theory on second language acquisition, followed by the possible phonological representations and analyses aligned with such perspective. Finally, the issue of second language phonology acquisition is revisited.

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21

Еськов, Valeriy Eskov, Филатова, and O. Filatova. "Other World, Other Science, Other Models in Complexity Descreaption." Journal of New Medical Technologies 21, no. 1 (June 4, 2014): 138–41. http://dx.doi.org/10.12737/3328.

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The understanding of very special systems of third type was created according to W.Weaver efforts. The new theory of chaos – self- organization was created last 40 years and was based on other understanding of stationary mode of third type of systems and its very specific chaotic behavior. The analog of the systems with physical system was discussed too. The third type of systems (opposite of deterministic and stochastic systems) was presented. It was discussed the principle distinguishes between dynamics of such system and traditional systems according to Heisenberg uncertainty principle. Traditional systems have certain and reproducible initial state of its system’s state vector and we can predict its future states. But in the third type of systems the authors have uncertain initial system state and uncertain vector states. It is a unique system which I.R. Prigogine in his famous article to the future generation determines as systems behind the science. The time for researching of such systems has come. For the modeling of biosystems, the authors propose method of quasi-attractor and define five special properties of complex systems. The main of it is connected with uninterrupted chaotic movements (glimmering property) of system’s vector in phase space of state and evolution of such system’s state vector in phase space of state. It was demonstrated that Heizenberg principle of uncertainty has special analog at theory of chaos – self organization. The botton boarder of the left side of inequality for the systems of third type the authors propose the value of quasiattractors, inside of it we chaos uninferrupled and chaotic movements of systems state vector. The value of quasiattractor determine like multiplication of coordinat x its speed dx/dt.

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22

VanderVen, Karen. "Chaos/Complexity Theory, Constructivism, Interdisciplinarity and Early Childhood Teacher Education." Journal of Early Childhood Teacher Education 18, no. 3 (September 1997): 43–48. http://dx.doi.org/10.1080/1090102970180305.

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23

Murphy, David. ""Chaos rules" revisited." International Review of Research in Open and Distributed Learning 12, no. 7 (November 25, 2011): 116. http://dx.doi.org/10.19173/irrodl.v12i7.1125.

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<p>About 20 years ago, lost in the midst of my PhD research, I mused over proposed titles. I was pretty pleased with myself to come up with ‘Chaos Rules’ (the implied double meaning was deliberate) or, more completely, <em>Chaos Rules: An Exploration of The Work of Instructional Designers in Distance Education</em>. I used the then emerging theories of chaos and complexity to underpin my analysis. So it was with not just a little excitement that I read the call for contributions to this Special Issue. What follows is a ‘walk through’ my thesis, with an emphasis on the contribution of chaos and complexity theory.</p><p> </p>

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24

Schweller, Randall L., and Roger Beaumont. "The Nazis' March to Chaos: The Hitler Era through the Lenses of Chaos-Complexity Theory." Journal of Military History 64, no. 4 (October 2000): 1184. http://dx.doi.org/10.2307/2677305.

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25

Arndt, Margarete, and Barbara Bigelow. "Commentary: The Potential of Chaos Theory and Complexity Theory for Health Services Management." Health Care Management Review 25, no. 1 (2000): 35–38. http://dx.doi.org/10.1097/00004010-200001000-00004.

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26

Korotkaya, Mariya. "New approaches in the study of competition: complexity theory." KANT 36, no. 3 (September 2020): 51–57. http://dx.doi.org/10.24923/2222-243x.2020-36.10.

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Competition has taken a rightful position in the subject field of modern economic science, based on traditional methods of research. New interdisciplinary theories emerged, such as complexity theory, aggregating synergies and chaos theory, autopoeus is theory and the theory of stable unbalanced systems and dissipative structures with other theoretic and methodological approaches. allows a new open to competition as a self-organized, dissipatative substance, having a spontaneous complication of its endogenous structures, as a tense, dynamic, autistic process, initially accumulating various alternatives.

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27

Jafari, Zahra, Ashraf Maibodi, and Muhammad Natsir. "A New Perspective: The Implication of Chaos/Complexity Theory in Language through Dichotomies." Randwick International of Education and Linguistics Science Journal 1, no. 3 (December 20, 2020): 372–77. http://dx.doi.org/10.47175/rielsj.v1i3.145.

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This study opens different points of view at chaos/complexity theory (C/CT) which is still a new theory in second language acquisition. Pro. Larsen-Freeman and her colleagues considered a variety of characteristics, C/CT is known as nonlinear dynamics or dynamical system theory that provides a framework for thinking about change over time. Scientists claim that one can see not only the laws of chaos but also those of order, through which a strong explanation for how any collection of components will organize itself and it can be generated in dichotomies. They attempt to rationalize the behavior of large and complex systems, believing they cannot be explained by usual rules of nature

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28

Wang, Yuling, Shubing Guo, and Shide Duan. "Computation of the Stability and Complexity about Triopoly Price Game Model with Delay Decision." Advances in Mathematical Physics 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/2717352.

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We develop the price game model based on the entropy theory and chaos theory, considering the three enterprises are bounded rationality and using the cost function under the resource constraints; that is, the yield increase will bring increased costs. The enterprises of new model adopt the delay decision with the delay parameters τ1 and τ2, respectively. According to the change of delay parameters τ1 and τ2, the bifurcation, stability, and chaos of the system are discussed, and the change of entropy when the system is far away from equilibrium is considered. Prices and profits are found to lose stability and the evolution of the system tends to the equilibrium state of maximum entropy. And it has a big fluctuation with the increase of τ1 and τ2. In the end, the chaos is controlled effectively. The entropy of the system decreases, and the interior reverts to order. The results of this study are of great significance for avoiding the chaos when the enterprises make price decisions.

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29

Brown, William S. "Corporate ethics initiatives as change management: lessons from complexity/chaos theory." International Journal of Management Concepts and Philosophy 3, no. 1 (2008): 82. http://dx.doi.org/10.1504/ijmcp.2008.018533.

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30

Yosifov, Alexander, Aditya Iyer, and Lachezar Filipov. "Holographic Interpretation of Relative State Complexity." Universe 6, no. 8 (July 22, 2020): 100. http://dx.doi.org/10.3390/universe6080100.

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We investigate a large-N conformal field theory (CFT) in a high-energy pure state coupled to a small auxiliary system of M weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, i.e., to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen’s approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large-N CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom.

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31

Weir, David. "Joyce, Chaos, and Complexity. Thomas Jackson Rice." Modern Philology 97, no. 4 (May 2000): 626–30. http://dx.doi.org/10.1086/492905.

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32

Hermanson, Scott. "Chaos and Complexity in Richard Powers'sThe Gold Bug Variations." Critique: Studies in Contemporary Fiction 38, no. 1 (October 1996): 38–51. http://dx.doi.org/10.1080/00111619.1996.9936497.

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33

Ying, Yiming, and Colin Campbell. "Rademacher Chaos Complexities for Learning the Kernel Problem." Neural Computation 22, no. 11 (November 2010): 2858–86. http://dx.doi.org/10.1162/neco_a_00028.

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We develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order 2 over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher chaos complexity by well-established metric entropy integrals and pseudo-dimension of the set of candidate kernels. Our new methodology mainly depends on the principal theory of U-processes and entropy integrals. Finally, we establish satisfactory excess generalization bounds and misclassification error rates for learning gaussian kernels and general radial basis kernels.

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34

Russell, Monica. "Deep Simplicity: Chaos, Complexity and the Emergence of Life." Pacific Conservation Biology 13, no. 1 (2007): 75. http://dx.doi.org/10.1071/pc070075a.

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The book Deep Simplicity is an introduction to chaos theory and the complex systems of the world. This book explains many concepts and physical laws associated with natural systems in a simple way. The author, Dr. John Gribbin, graduated with a degree in astrophysics from the University of Cambridge and is currently a visiting Fellow in astronomy at the University of Sussex. He has worked for the science journal Nature and the magazine New Scientist (for which he is now a physics consultant); some of his books include In search of Schr�dinger?s Cat (1984). In Search of the Big Bang (1986) and Fate of the Universe (1987).

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Guo, Shubing, Junhai Ma, and Xueli Zhan. "Complexity and Application of Tobacco Manufacturer Pricing Game considering Market Segments." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6701286.

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This paper considers price as a strategy using two methods of market segmentation through game theory based on the collected data of several typical cities in Shandong province. Three oligarchs are discussed to analyze the complexity of the market in tobacco system. The effect of different factors on the equilibrium price of Nash equilibrium is discussed. What is more, the variation of parameters drives the system to change to uncertain status, even to bifurcation or chaos. We also discuss the model under normal circumstances, when the three parties jointly take chaos control measures, and its impact on the system. Finally, we clarify chaos control of economic significance. The results indicate that only reasonable pricing strategy is a critical point to achieve maximized profit and maintain orderly operation at the same time, which is a constructive suggestion for tobacco companies’ operational strategy.

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Yi-min, Huang, Li Qiu-xiang, and Zhang Yu-hao. "The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern." Complexity 2018 (December 2, 2018): 1–15. http://dx.doi.org/10.1155/2018/9216193.

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This paper, considering risk aversion and fair concern, establishes a dynamic price game model of a dual-channel supply chain in which dual-channel retailer sells products through traditional channel and online channel and the online retailer only sells products through online channel. The stability of the system and the influences of different parameter values on utilities are analyzed emphatically using game theory and nonlinear dynamic theory, such as 2D and 3D bifurcation diagram, parameter plot basin, chaos attractor, and sensitivity to initial value. The results find that the system is more likely to lose stability and fall into chaos with the customer demand fluctuating greatly. The system enters into chaos through flip bifurcation with the increase of the price adjustment speed; adjusting the risk-aversion levels or the fairness concern levels of the two retailers can make the system be in a stable state or delay the occurrence of system instability. When the system is in chaos, the average utility of the online retailer will decrease and one of the dual-channel retailers will increase. Using the state feedback control method, the system can return to a stable state from chaos by selecting appropriate control parameters. The research of this paper is of great significance to the decision-makers’ price decision and supply chain operation management.

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YANG, LEI, WEI PAN, LIAN SHAN YAN, BIN LUO, SHUI YING XIANG, and NING JIANG. "COMPLEXITY AND SYNCHRONIZATION IN CHAOTIC INJECTION-LOCKING SEMICONDUCTOR LASERS." Modern Physics Letters B 25, no. 26 (October 20, 2011): 2061–67. http://dx.doi.org/10.1142/s021798491102725x.

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The chaotic complexity properties of semiconductor lasers in the chaotic synchronization systems are investigated numerically, based on the information theory based quantifier, the permutation entropy (PE). We find that, on the one hand, the degree of complexity for the master laser increases with the feedback strength firstly and then saturate at higher feedback strength, but are hardly affected by the feedback delay. On the other hand, for the slave laser, the complexity degree is closer to that for the master laser when the high quality chaos synchronization is obtained, which shows that, the PE method is a successful quantifier to evaluate the degree of complexity for the chaotic signals in chaos synchronization systems, and can be considered as a complementary tool to observe the synchronization quality.

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Houston, Renée. "Participation as chaos: Lessons from the principles of complexity theory for democracy." World Futures 57, no. 4 (July 2001): 315–38. http://dx.doi.org/10.1080/02604027.2001.9972837.

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BRACK, CATHERINE J., GREG BRACK, and ANDREA ZUCKER. "How Chaos and Complexity Theory Can Help Counselors to Be More Effective." Counseling and Values 39, no. 3 (April 1995): 200–208. http://dx.doi.org/10.1002/j.2161-007x.1995.tb00942.x.

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40

Bloch, Deborah P. "Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory." Career Development Quarterly 53, no. 3 (March 2005): 194–207. http://dx.doi.org/10.1002/j.2161-0045.2005.tb00990.x.

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41

Abu Elwan, Reda. "The Effect of Teaching "Chaos Theory and Fractal Geometry" on Geometric Reasoning Skills of Secondary Students." INTERNATIONAL JOURNAL OF RESEARCH IN EDUCATION METHODOLOGY 6, no. 2 (August 30, 2015): 804–15. http://dx.doi.org/10.24297/ijrem.v6i2.3876.

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Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. Chaos theory is the qualitative study of unstable periods in deterministic nonlinear dynamical systems, chaos theory looks at how things evolve. Fractal geometry is a subject that has established connections with many areas of mathematics (including number theory, probability theory and dynamical systems). Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century; this paper investigate the concepts of chaos theory and fractal geometry as a conceptual transformation at secondary school level. This paper reports a study of the effects of teaching chaos theory and fractal geometry on geometric reasoning skills in geometry. Thirty of the tenth grade students of basic education participated in an experimental group, which was involved in working with chaos theory and fractal geometry activities, pre-treatment measures the geometric Reasoning skills. Teaching fractal geometry properties and examples were focused in the teaching activities. At the end of the teaching measuresÂ geometric reasoning skills were again obtained. Since the study was an exploration, the effectiveness of teaching chaos theory and fractal geometry, the exploratory data collected by the researcher was also considered to be an important part of the study.Â

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Sharma, Vijay. "Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier." Open Cardiovascular Medicine Journal 3, no. 1 (September 10, 2009): 110–23. http://dx.doi.org/10.2174/1874192400903010110.

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Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

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West, Bruce J. "Sir Isaac Newton Stranger in a Strange Land." Entropy 22, no. 11 (October 25, 2020): 1204. http://dx.doi.org/10.3390/e22111204.

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The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be incompatible with Newton’s unquestioning reliance on an absolute space and time upon which he built his discrete calculus.

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Горбунов, D. Gorbunov, Эльман, Kseniya Elman, Гавриленко, T. Gavrilenko, Григоренко, and V. Grigorenko. "Features stochastics and chaos theory processing myogram." Complexity. Mind. Postnonclassic 4, no. 1 (August 23, 2015): 45–53. http://dx.doi.org/10.12737/10864.

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In studies using the method of multi-dimensional phase space. In the study and modeling of complex biological objects (complexity) there is the possibility of introducing traditional physical methods in biological research and new methods based on chaos theory, self-organization. The paper shows the feasibility of applying the method of multi-dimensional phase space as a quantitative measure for the evaluation of chaotic dynamics on the example of the muscles (flexor of the little finger). As a measure of the state of the neuromuscular system of the person (weak muscle tension and strong, almost the maximum force) used quasi-attractors volumes of multidimensional phase space. This enables identification of the actual measurements of the parameters of the functional state with weak muscles (p = 5th Dan) and strong (P = 10 daN) static stress. Was built timebase signal obtained with myograph and were built autocorrelation function A (t) signal. In the end analysis of the biomechanical system based on a comparison of volume quasi-attractor, as well as on the basis of analysis of the Shannon entropy N. kzvaziattraktora volume displacement at low load is slightly less than the same amount of displacement under a heavy load of flexor muscles of the little finger, just as the values of the Shannon entropy at a heavy load is increased as compared with the values obtained by the weak muscle load.

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Manera, Maurizio. "Perspectives on Complexity, Chaos and Thermodynamics in Environmental Pathology." International Journal of Environmental Research and Public Health 18, no. 11 (May 27, 2021): 5766. http://dx.doi.org/10.3390/ijerph18115766.

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Though complexity science and chaos theory have become a common scientific divulgation theme, medical disciplines, and pathology in particular, still rely on a deterministic, reductionistic approach and still hesitate to fully appreciate the intrinsic complexity of living beings. Herein, complexity, chaos and thermodynamics are introduced with specific regard to biomedical sciences, then their interconnections and implications in environmental pathology are discussed, with particular regard to a morphopathological, image analysis-based approach to biological interfaces. Biomedical disciplines traditionally approach living organisms by dissecting them ideally down to the molecular level in order to gain information about possible molecule to molecule interactions, to derive their macroscopic behaviour. Given the complex and chaotic behaviour of living systems, this approach is extremely limited in terms of obtainable information and may lead to misinterpretation. Environmental pathology, as a multidisciplinary discipline, should grant privilege to an integrated, possibly systemic approach, prone to manage the complex and chaotic aspects characterizing living organisms. Ultimately, environmental pathology should be interested in improving the well-being of individuals and the population, and ideally the health of the entire ecosystem/biosphere and should not focus merely on single diseases, diseased organs/tissues, cells and/or molecules.

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TANG, CHANGBING, FANGYUE CHEN, JIANBO WANG, and XIANG LI. "EXTENDING LOCAL PASSIVITY THEORY AND HOPF BIFURCATION AT THE EDGE OF CHAOS IN OREGONATOR CNN." International Journal of Bifurcation and Chaos 22, no. 11 (November 2012): 1250285. http://dx.doi.org/10.1142/s0218127412502859.

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The fundamental local passivity theory asserts that a wide spectrum of complex behaviors may exist if the cells in the reaction–diffusion are not locally passive. This local passivity principle has provided a powerful tool for studying the complexity in a homogeneous lattice formed by coupled cells. In this paper, the complexity matrix YQ(s), which is the tool for testing the local passivity theory, is modified based on the characteristic polynomial AQ(λ). Then, the local passivity theory is applied to the study of the Oregonator CNN to judge if the cell parameters of a CNN are chosen at the edge of chaos. Analysis of the bifurcation and the numerical simulations show that nonzero diffusion term in Oregonator CNN may cause a reaction–diffusion equation oscillating under the appropriate choice of diffusion coefficient if the local passivity theory is not satisfied. That is, if the cell parameters of a CNN are chosen at the edge of chaos, the system is potentially unstable.

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Sade, Liliane Assis. "Complexity and identity reconstruction in second language acquisition." Revista Brasileira de Linguística Aplicada 9, no. 2 (2009): 515–37. http://dx.doi.org/10.1590/s1984-63982009000200008.

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The participation of the individual in different discursive practices contributes to the social formation of identity which is not only constituted, but also, fractalized and emerged via discourse. Taking the concept of polyphony, proposed by Bakhtin (1981, 1986), this work intends to discuss the social formation of the self and the emergence of multiple identities through the perspective of Complexity Theory. Borrowing the concepts of attractors, bifurcation points and fractals from Chaos Theory, and relating them to identity issues, this paper shows how the acknowledgement of identity as a complex/chaotic system can be useful to a deeper understanding of the language acquisition process. Some narratives of AMFALE project are used in order to exemplify the theoretical issues proposed.

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Goldberger, A. L. "Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside." Lancet 347, no. 9011 (May 1996): 1312–14. http://dx.doi.org/10.1016/s0140-6736(96)90948-4.

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Mouck, T. "Capital markets research and real world complexity: The emerging challenge of chaos theory." Accounting, Organizations and Society 23, no. 2 (February 1998): 189–215. http://dx.doi.org/10.1016/s0361-3682(97)00004-4.

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Farsi, Roghayeh. "Chaos/Complexity Theory and Postmodern Poetry: A Case Study of Jorie Graham’s “Fuse”." SAGE Open 7, no. 3 (July 2017): 215824401772513. http://dx.doi.org/10.1177/2158244017725130.

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