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REFERENCES

  • 1
    Mackey,M.C.;Glass,L.Oscillation and chaos in physiological control systems.Science1977,197,287289.
  • 2
    Doyne Farmer,J.Chaotic attractors of an infinite-dimensional dynamical system.Phys D: Nonlinear Phenom1982,4,366393.
  • 3
    Dorizzi,B.;Grammaticos,B.;Le Berre,M.;Pomeau,Y.;Ressayre,E.;Tallet,A.Statistics and dimension of chaos in differential delay systems.Phys Rev A1987,35,328339.
  • 4
    Yanchuk,S.;Perlikowski,P.Delay and periodicity.Phys Rev E2009,79,046221.
  • 5
    Voss,H.U.Anticipating chaotic synchronization.Phys Rev E2000,61,51155119.
  • 6
    Packard,N.H.Adaptation toward the edge of chaos. In:Dynamic Patterns in Complex Systems;Kelso,A.S.;Mandell,A.J.;Shlesinger,M.F., Eds.;World Scientific Pub Co Inc.:Singapore,1988; pp.293301.
  • 7
    Mitchell,M.;Hraber,P.T.;Crutchfield,J.P.Revisiting the edge of chaos: Evolving cellular automata to perform computations.Complex Syst1993,7,89130.
  • 8
    Kauffman,S.A.;Johnsen,S.Coevolution to the edge of chaos: Coupled fitness landscapes, poised states, and coevolutionary avalanches.J Theor Biol1991,149,467505.
  • 9
    Pierre,D.;Hübler,A.A theory for adaptation and competition applied to logistic map dynamics.Phys D: Nonlinear Phenom1994,75,343360.
  • 10
    Hübler,A.W.;Wotherspoon,T.Self-adjusting systems avoid chaos.Complexity2009,14,811.
  • 11
    Melby,P.;Kaidel,J.;Weber,N.;Hübler,A.Adaptation to the edge of chaos in the self-adjusting logistic map.Phys Rev Lett2000,84,59915993.
  • 12
    Chua,L.;Komuro,M.;Matsumoto,T.The double scroll family.IEEE Trans Circuits Syst1986,33,10721118.
  • 13
    Baym,M.;Hübler,A.W.Conserved quantities and adaptation to the edge of chaos.Phys Rev E2006,73,056210056217.
  • 14
    Langton,C.G.Computation at the edge of chaos: Phase transitions and emergent computation.Phys D1990,42,1237.
  • 15
    Crutchfield,J.P.;Young,K.Computation at the onset of chaos. In:Entropy, Complexity, and the Physics of Information, SFI Studies in the Sciences of Complexity,VIII;Zurek,W., Ed.;Addison-Wesley:Reading, MA,1990; pp.223269.
  • 16
    Hübler,A.W.;Phelps,K.C.Guiding an adaptive system through chaos.Complexity2007,13,6266.
  • 17
    Ando,H.;Aihara,K.Adaptation to the edge of chaos in one-dimensional chaotic maps.Phys Rev E2006,74,066205.
  • 18
    Sinha,S.;Parthasarathy,S.Unusual dynamics of extinction in a simple ecological model.Proc Nat Acad Sci1996,93,15041508.
  • 19
    Kauffman,S.A.The Origins of Order: Self-Organization and Selection in Evolution;Oxford University Press:New York, NY,1993.
  • 20
    Bertschinger,N.;Natschläger,T.Real-time computation at the edge of chaos in recurrent neural networks.Neural Comput2004,16,14131436.
  • 21
    Schürmann,F.;Meier,K.;Schemmel,J.Edge of chaos computation in mixed-mode vlsi—A hard liquid. In:Advances in Neural Information Processing Systems17;Saul,L.K.;Weiss,Y.;Bottou,L., Eds.;MIT Press:Cambridge, MA,2005; pp.12011208.
  • 22
    Mitchell,M.;Crutchfield,J.P.;Hraber,P.T.Dynamics, Computation, and the “Edge of Chaos”: A Re-Examination;Perseus Books:Cambridge, MA, USA,1999.
  • 23
    Pantaleone,J.Synchronization of metronomes.Am J Phys2002,70,9921000.
  • 24
    Bragin,V.;Vagaitsev,V.;Kuznetsov,N.;Leonov,G.Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits.J Comp Syst Sci Int2011,50,511543. 10.1134/S106423071104006X.
  • 25
    Leonov,G.A.;Kuznetsov,N.V.;Vagaitsev,V.I.Localization of hidden chua's attractors.Phys Lett A2011,375,22302233.
  • 26
    Bryan,J.A.Investigating the conservation of mechanical energy using video analysis: Four cases.Phys Edu2010,45,5057.
  • 27
    Aubert,D.;Thorpe,C. Color image processing for navigation: Two road trackers, Technical Report CMU-RI-TR-90–09, Robotics Institute: Pittsburgh, PA, April1990.
  • 28
    Ulrichs,H.;Mann,A.;Parlitz,U.Synchronization and chaotic dynamics of coupled mechanical metronomes.Chaos2009,19,043120.
  • 29
    Andronov,A.A.;Khaikin,S.E.Theory of Oscillations (in Russian);Gostekhizdat:Moscow,1937.
  • 30
    Andronov,A.A.;Vitt,A.A.;Khaikin,S.E.Theory of Oscillations;Courier Dover Publications:Mineola, NY,1987.
  • 31
    Appleton,E.V.The automatic synchronization of triode oscillators.Proc Cambridge Philos Soc (Math Phys Sci)1922,21,231248.
  • 32
    van der Pol,B.A theory of the amplitude of free and forced triode vibrations.Radio Review1920,1,701710,754–762.
  • 33
    van der Pol,B.Forced oscillations in a circuit with non-linear resistance (reception with reactive triode).J Sci Ser.71927,3,6580.
  • 34
    Pikovsky,A.;Rosenblum,M.;Kurths,J.Synchronization: A Universal Concept in Nonlinear Science;Cambridge University Press:Cambridge, UK,2002.
  • 35
    Rayleigh,R.J.S.The Theory of Sound, Vol.2;MacMillan:London, UK,1896.
  • 36
    Abel,M.;Ahnert,K.;Bergweiler,S.Synchronization of sound sources.Phys Rev Lett2009,103,114301.
  • 37
    Strogatz,S.H.Sync: The Emerging Science of Spontaneous Order;Hyperion Press:New York, NY,2003.
  • 38
    Fujisaka,H.;Yamada,T.Stability theory of synchronized motion in coupled-oscillator systems.Pro Theo Phys1983,69,3247.
  • 39
    Pecora,L.M.;Carroll,T.L.Synchronization in chaotic systems.Phys Rev Lett1990,64,821824.
  • 40
    Pecora,L.M.;Carroll,T.L.Driving systems with chaotic signals.Phys Rev A1991,44,23742383.
  • 41
    de Sousa Vieira,M.;Lichtenberg,A.J.;Lieberman,M.A.Synchronization of regular and chaotic systems.Phys Rev A1992,46,R7359R7362.
  • 42
    Senator,M.Synchronization of two coupled escapement-driven pendulum clocks.J Sound Vibrat2006,291,566603.
  • 43
    Blekhman,I.I.Synchronization in Science and Technology;ASME Press:New York,1988.
  • 44
    Bennett,M.;Schatz,M.F.;Rockwood,H.;Wiesenfeld,K.Huygens's clocks. Proc Royal Society of London.Series A: Mathe, Phys Eng Sci2002,458,563579.
  • 45
    Eccles,W.H. Method of producing compound radiation fields by multiple antennae systems and the employment of a master oscillator. British Patent184282 May1921.
  • 46
    Eccles,W.H.Studies from a wireless laboratory.Electrician1923,89,195214.
  • 47
    Néda,Z.;Ravasz,E.;Brechet,Y.;Vicsek,T.;Barabási,A.-L.Self-organizing processes: The sound of many hands clapping.Nature2000,403,849850.
  • 48
    Rosenblum,M.;Pikovsky,A.Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators.Contemp Phys2003,44,401416.
  • 49
    Kuznetsov,N.V.;Leonov,G.A.;Nijmeijer,H.;Pogromski,A.Y.Synchronization of two metronomes. In: InIFAC Proceedings Volumes (IFAC-PapersOnline), Vol.3,2007; pp.4952.
  • 50
    Czolczynski,K.;Perlikowski,P.;Stefanski,A.;Kapitaniak,T.Clustering and synchronization of n huygens' clocks.Phys A: Stat Mech Appl2009,388,50135023.
  • 51
    Dallard,P.;Fitzpatrick,A.J.;Flint,A.;Le Bourva,S.;Low,A.;Ridsdill Smith,R.M.;Wilford,M.The London millennium footbridge.Struct Eng2001,79,1735.
  • 52
    Strogatz,S.H.;Abrams,D.M.;McRobie,A.;Eckhardt,B.;Ott,E.Crowd synchrony on the millennium bridge.Nature2005,438,4344.
  • 53
    Pogromsky,A.Y.Synchronization and adaptive synchronization in semi-passive systems. In: In1st International Conference on Control of Oscillations and Chaos, Vol.1:St. Petersburg, Russia, August1997; pp.6468.
  • 54
    Blekhman,I.I.;Fradkov,A.L.;Nijmeijer,H.;Pogromsky,A.Y.On self-synchronization and controlled synchronization.Syst Control Lett1997,31,299305.
  • 55
    Hodge,S.J.;Bell,M.B.V.;Cant,M.A.Reproductive competition and the evolution of extreme birth synchrony in a cooperative mammal.Biol Lett2010,7,5456.
  • 56
    Chen,M.;Kurths,J.Synchronization of time-delayed systems.Phys Rev E2007,76,036212.
  • 57
    Pikovsky,A.;Rosenblum,M.;Kurths,J.Phase synchronization in regular and chaotic systems.Int J Bifurcation Chaos2000,10,22912305.
  • 58
    Barahona,M.;Pecora,L.M.Synchronization in small-world systems.Phys Rev Lett2002,89,054101.
  • 59
    Chavez,M.;Hwang,D.U.;Amann,A.;Hentschel,H.G.;Boccaletti,S.Synchronization is enhanced in weighted complex networks.Phys Rev Lett2005,94,218701.
  • 60
    Tonjes,R.;Masuda,N.;Kori,H.Synchronization transition of identical phase oscillators in a directed small-world network.Chaos2010,20,033108.
  • 61
    Lu,X.B.;Wang,X.F.;Li,X.;Fang,J.Q.Synchronization in weighted complex networks: Heterogeneity and synchronizability.Phys A: Statist Mech Appl2006,370,381389.
  • 62
    Chavez,M.;Hwang,D.-U.;Amann,A.;Boccaletti,S.Synchronizing weighted complex networks.Chaos2006,16,015106.
  • 63
    Chavez,M.;Hwang,D.-U.;Martinerie,J.;Boccaletti,S.Degree mixing and the enhancement of synchronization in complex weighted networks.Phys Rev E2006,74,066107.
  • 64
    Boccaletti,S.;Hwang,D.-U.;Chavez,M.;Amann,A.;Kurths,J.;Pecora,L.M.Synchronization in dynamical networks: Evolution along commutative graphs.Phys Rev E2006,74,016102.
  • 65
    Rosenblum,M.G.;Pikovsky,A.S.;Kurths,J.Phase synchronization of chaotic oscillators.Phys Rev Lett1996,76,18041807.
  • 66
    Mormann,F.;Kreuz,T.;Andrzejak,R.G.;David,P.;Lehnertz,K.;Elger,C.E.Epileptic seizures are preceded by a decrease in synchronization.Epilepsy Res2003,53,173185.
  • 67
    Lehnertz,K.;Bialonski,S.;Horstmann,M.-T.;Krug,D.;Rothkegel,A.;Staniek,M.;Wagner,T.Synchronization phenomena in human epileptic brain networks.J Neurosci Methods2009,183,4248.
  • 68
    Strogatz,S.H.Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering;Westview Press, Studies in Non-Linearity:Cambridge, MA,2001.