Whats the application of Hyperchaotic system? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T03:51:59Z http://mathoverflow.net/feeds/question/74289 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/74289/whats-the-application-of-hyperchaotic-system Whats the application of Hyperchaotic system? Vinaya Shrestha 2011-09-01T20:15:55Z 2012-11-18T15:27:40Z <p>Can anyone tell me where hyperchaotic system is used in real world, its applications? It'd be great if you could provide a literature to back any application as well. Thanks.</p> http://mathoverflow.net/questions/74289/whats-the-application-of-hyperchaotic-system/74292#74292 Answer by Carlo Beenakker for Whats the application of Hyperchaotic system? Carlo Beenakker 2011-09-01T21:01:38Z 2011-09-01T21:45:34Z <p><a href="http://www.scholarpedia.org/article/Hyperchaos#Experimental_hyperchaotic_behaviors" rel="nofollow">http://www.scholarpedia.org/article/Hyperchaos#Experimental_hyperchaotic_behaviors</a></p> <p>and some more pointers:</p> <ul> <li><p>C. Stan, C.P. Cristescu, and D. Alexandroaei, Chaos and hyperchaos in a symmetrical discharge plasma: experiment and modelling, University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, vol. 70 (4), 25-30 (2008).</p></li> <li><p>R. Stoop et al., A p-Ge semiconductor experiment showing chaos and hyperchaos, Physica D, vol. 35 (3), 425-435 (1989).</p></li> <li><p>T. Matsumoto, L. Chua, and K. Kobayashi, Hyperchaos - Laboratory experiment and numerical confirmation, IEEE Transactions On Circuits And Systems, vol. 33 (11), 1143-1147 (1986).</p></li> </ul> http://mathoverflow.net/questions/74289/whats-the-application-of-hyperchaotic-system/112768#112768 Answer by RH for Whats the application of Hyperchaotic system? RH 2012-11-18T15:27:40Z 2012-11-18T15:27:40Z <p>It is well known that if two or more Lyapunov exponents of a dynamical system are positive throughout a range of parameter space, then the resulting attractors are hyperchaotic. The importance of these attractors is that they are less regular and are seemingly "almost full" in space, which explains their importance in fluid mixing [Scheizer &amp; Hasler, 1996, Abel et al., 1997, Ottino,1989; Ottino et al., 1992]. See:</p> <p>Abel. A, Bauer. A, Kerber. K, Schwarz. W, [1997] " Chaotic codes for CDMA application," Proc. ECCTD '97, 1, 306.</p> <p>Kapitaniak.T, Chua. L. O, Zhong. Guo-Qun, [1994] " Experimental hyperchaos in coupled Chua's circuits," Circuits,.Syst. I: Fund. Th. Appl. 41 (7), 499 -- 503.</p> <p>Ottino. J. M, [1989] " The kinematics of mixing: stretching, chaos, and transport," Cambridge: Cambridge University Press.</p> <p>Ottino. J. M, Muzzion. F. J, Tjahjadi. M, Franjione.J. G, Jana. S. C, Kusch. H. A, [1992] " Chaos, symmetry, and self-similarity: exploring order and disorder in mixing processes," Science. 257, 754--760.</p> <p>Scheizer. J, Hasler. M, [1996] " Multiple access communication using chaotic signals," Proc. IEEE ISCAS '96. Atlanta, USA, 3, 108.</p> <p>Thamilmaran. K, Lakshmanan. M, Venkatesan. A, [2004] " Hyperchaos in a Modified Canonical Chua's Circuit," Int. J. Bifurcation and Chaos. 14 (1),221--244.</p>