Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.

share|improve this question
add comment

2 Answers

up vote 2 down vote accepted

http://www.scholarpedia.org/article/Hyperchaos#Experimental_hyperchaotic_behaviors

and some more pointers:

  • 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).

  • R. Stoop et al., A p-Ge semiconductor experiment showing chaos and hyperchaos, Physica D, vol. 35 (3), 425-435 (1989).

  • 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).

share|improve this answer
    
i found this as well, i wanted some published papers or book chapters that showed applications of hyperchaos –  Vinaya Shrestha Sep 1 '11 at 21:13
add comment

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 & Hasler, 1996, Abel et al., 1997, Ottino,1989; Ottino et al., 1992]. See:

Abel. A, Bauer. A, Kerber. K, Schwarz. W, [1997] " Chaotic codes for CDMA application," Proc. ECCTD '97, 1, 306.

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.

Ottino. J. M, [1989] " The kinematics of mixing: stretching, chaos, and transport," Cambridge: Cambridge University Press.

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.

Scheizer. J, Hasler. M, [1996] " Multiple access communication using chaotic signals," Proc. IEEE ISCAS '96. Atlanta, USA, 3, 108.

Thamilmaran. K, Lakshmanan. M, Venkatesan. A, [2004] " Hyperchaos in a Modified Canonical Chua's Circuit," Int. J. Bifurcation and Chaos. 14 (1),221--244.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.