[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki5\/chaotic-hysteresis-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki5\/chaotic-hysteresis-wikipedia\/","headline":"Chaotic hysteresis – Wikipedia","name":"Chaotic hysteresis – Wikipedia","description":"From Wikipedia, the free encyclopedia A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory)","datePublished":"2022-03-08","dateModified":"2022-03-08","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki5\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki5\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/en.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","url":"https:\/\/en.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","height":"1","width":"1"},"url":"https:\/\/wiki.edu.vn\/en\/wiki5\/chaotic-hysteresis-wikipedia\/","wordCount":1012,"articleBody":"From Wikipedia, the free encyclopediaA nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis.  As the latter involves the persistence of a state, such as magnetization, after the causal or exogenous force or factor is removed, it involves multiple equilibria for given sets of control conditions.  Such systems generally exhibit sudden jumps from one equilibrium state to another (sometimes amenable to analysis using catastrophe theory). If chaotic dynamics appear either prior to or just after such jumps, or are persistent throughout each of the various equilibrium states, then the system is said to exhibit chaotic hysteresis.  Chaotic dynamics are irregular and bounded and subject to sensitive dependence on initial conditions.Background and applications[edit]The term was introduced initially by Ralph Abraham and Christopher Shaw (1987), but was modeled conceptually earlier and has been applied to a wide variety of systems in many disciplines.  The first model of such a phenomenon was due to Otto R\u00f6ssler in 1983, which he viewed as applying to major brain dynamics, and arising from three-dimensional chaotic systems.  In 1986 it was applied to electric oscillators by Newcomb and El-Leithy, perhaps the most widely used application since (see also Pecora and Carroll, 1990).The first to use the term for a specific application was J. Barkley Rosser, Jr. in 1991, who suggested that it could be applied to explaining the process of systemic economic transition, with Poirot (2001) following up on this in regard to the Russian financial crisis of 1998. Empirical analysis of the phenomenon in the Russian economic transition was done by Rosser, Rosser, Guastello, and Bond (2001).  While he did not use the term, T\u00f6nu Puu (1989) presented a multiplier-accelerator business cycle model with a cubic accelerator function that exhibited the phenomenon.Other conscious applications of the concept have included to Rayleigh-B\u00e9nard convection rolls, hysteretic scaling for ferromagnetism, and a pendulum on a rotating table (Berglund and Kunz, 1999), to induction motors (S\u00fato and Nagy, 2000), to combinatorial optimization in integer programming (Wataru and Eitaro, 2001), to isotropic magnetization (Hauser, 2004), to bursting oscillations in beta cells in the pancreas and population dynamics (Fran\u00e7oise and Piquet, 2005), to thermal convection (Vadasz, 2006), and to neural networks (Liu and Xiu, 2007).References[edit]Ralph H. Abraham and Christopher D. Shaw. \u201cDynamics: A Visual Introduction.\u201d In F. Eugene Yates, ed., Self-Organizing Systems: The Emergence of Order. New York: Plenum Press, pp.\u00a0543\u2013597, 1987.Otto E. R\u00f6ssler. \u201cThe Chaotic Hierarchy.\u201d Zeitschrift f\u00fcr Natuforschung 1983, 38a, pp.\u00a0788\u2013802.R.W. Newcomb and N. El-Leithy. \u201cChaos Generation Using Binary Hysteresis.\u201d Circuits, Systems, and Signal Processing September 1986, 5(3), pp.\u00a0321\u2013341.L.M. Pecora and T.L. Carroll. \u201cSynchronization in Chaotic Systems.\u201d Physical Review Letters February 19, 1990, 64(8), pp.\u00a0821\u2013824.J. Barkley Rosser, Jr. From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Boston\/Dordrecht: Kluwer Academic Publishers, Chapter 17, 1991.Clifford S. Poirot. \u201cFinancial Integration under Conditions of Chaotic Hysteresis: The Russian Financial Crisis of 1998.\u201d Journal of Post Keynesian Economics Spring 2001, 23(3), pp.\u00a0485\u2013508.J. Barkley Rosser, Jr., Marina V. Rosser, Stephen J. Guastello, and Robert W. Bond, Jr. \u201cChaotic Hysteresis and Systemic Economic Transformation: Soviet Investment Patterns.\u201d Nonlinear Dynamics, Psychology, and Life Sciences October 2001, 5(4), pp.\u00a0545\u2013566.T\u00f6nu Puu. Nonlinear Economic Dynamics. Berlin: Springer-Verlag, 1989.N. Berglund and H. Kunz. \u201cMemory Effects and Scaling Laws in Slowly Driven Systems.\u201d Journal of Physics A: Mathematical and General January 8, 1999, 32(1), pp.\u00a015\u201339.Zolt\u00e1n S\u00fato and Istv\u00e1n Nagy. \u201cStudy of Chaotic and Periodic Behaviours of a Hysteresis Current Controlled Induction Motor Drive.\u201d In Hajime Tsuboi and Istv\u00e1n Vajda, eds., Applied Electromagnetics and Computational Technology II. Amsterdam: IOS Press, pp.\u00a0233\u2013243.Murano Wataru and Aiyoshi Eitaro. \u201cOpening Door toward 21st Century. Integer Programming by the Multi-Valued Hysteresis Machines with the Chaotic Properties.\u201d Transactions of the Institute of Electrical Engineers of Japan C 2001, 121(1), pp.\u00a076\u201382.Hans Hauser. \u201cEnergetic Model of Ferromagnetic Hysteresis: Isotropic Magnetization.\u201d Journal of Applied Physics September 1, 2004, 96(5), pp.\u00a02753\u20132767.J.P. Fran\u00e7oise and C. Piquet. \u201cHysteresis Dynamics, Bursting Oscillations and Evolution to Chaotic Regimes.\u201d Acta Biotheoretica 2005, 53(4), pp.\u00a0381\u2013392.P. Vadasz. \u201cChaotic Dynamics and Hysteresis in Thermal Convection.\u201d Journal of Mechanical Engineering Science \u201c 2006, 220(3), pp. 309-323.Xiangdong Liu and Chunko Xiu. \u201cHysteresis Modeling Based on the Hysteretic Chaotic Neural Network.\u201d Neural Computing Applications online October 30, 2007: http:\/\/www.springerlink.com\/content\/x76777476785m48[permanent dead link]."},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki5\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki5\/chaotic-hysteresis-wikipedia\/#breadcrumbitem","name":"Chaotic hysteresis – Wikipedia"}}]}]