ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov S. P. Electronic circuits manifesting hyperbolic chaos and simulation of their dynamics using software package multisim. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 5, pp. 98-115. DOI: 10.18500/0869-6632-2011-19-5-98-115

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Electronic circuits manifesting hyperbolic chaos and simulation of their dynamics using software package multisim

Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

We consider several electronic circuits, which are represented dynamical systems with hyperbolic chaotic attractors, such as Smale–Williams and Plykin attractors, and present results of their simulation using the software package NI Multisim 10. The approach developed is useful as an intermediate step of constructing real electronic devices with structurally stable hyperbolic chaos, which may be applicable in systems of secure communication, noise radar, for cryptographic systems, for random number generators. The developed approach is also of methodological interest for training students specializing in radiophysics and nonlinear dynamics in the design and analysis of systems with complex dynamics on a base of examples close to practical applications.

  1. Andronov AA, Vitt AA, Khaikin SE. Theory of Oscillators. Pergamon; 1966. 848 p.
  2. Rabinovich MI, Trubetskov DI. Oscillations and Waves in Linear and Nonlinear Systems. Dordrecht: Springer; 1989. 578 p. DOI: 10.1007/978-94-009-1033-1.
  3. Shilnikov L. Mathematical problems of nonlinear dynamics: A tutorial. Int. J. Bifurcation Chaos. 1997;7(9):1953–2001. DOI: 10.1142/S0218127497001527.
  4. Smale S. Differentiable dynamical systems. Bull. Amer. Math. Soc. (NS). 1967;73(6):747–817.
  5. Sinai YG. Stochasticity of dynamical systems. In: Gaponov-Grekhov AV, editor. Nonlinear Waves. Moscow: Nauka; 1979. P. 192–212 (in Russian).
  6. Afraimovich V, Hsu SB. Lectures on chaotic dynamical systems, AMS/IP Studies in Advanced Mathematics. Vol. 28. American Mathematical Society. Providence, RI: International Press, Somerville, MA; 2003. 353 p.
  7. Katok A, Hasselblat B. Introduction to the Modern Theory of Dynamical Systems. Cambridge: Cambridge University Press; 1995. 802 p. DOI: 10.1017/CBO9780511809187.
  8. Loskutov AY. Fascination of chaos. Phys. Usp. 2010;53(12):1257–1280. DOI: 10.3367/UFNe.0180.201012d.1305.
  9. Anishchenko VS, Astakhov VV, Vadivasova TE, Neiman AB, Strelkova GI, Schimansky-Geier L. Nonlinear Effects in Chaotic and Stochastic Systems. Moscow – Izhevsk: Institute of Computer Research; 2003. 529 p. (in Russian).
  10. Barreira L, Pesin Y. Lectures on Lyapunov exponents and smooth ergodic theory. In: Smooth Ergodic Theory and Its Applications. AMS, Proceedings of Symposia in Pure Mathematics; 2001. P. 3.
  11. Bonatti C, Diaz LJ, Viana M. Dynamics beyond uniform hyperbolicity. A global geometric and probobalistic perspective. Encyclopedia of Mathematical Sciences. Vol. 102. Springer: Berlin, Heidelberg, New-York; 2005. 384 p. DOI: 10.1007/b138174.
  12. Kuznetsov SP. Example of a physical system with a hyperbolic attractor of the Smale–Williams type. Phys. Rev. Lett. 2005;95(14):144101. DOI: 10.1103/PhysRevLett.95.144101.
  13. Kuznetsov AP, Sataev IR. Verification of hyperbolicity conditions for a chaotic attractor in a system of coupled nonautonomous van der Pol oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2006;14(5):3–29 (in Russian). DOI: 10.18500/0869-6632-2006-14-5-3-29.
  14. Kuznetsov SP, Seleznev EP. A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system. Journal of Experimental and Theoretical Physics. 2006;102(2):355–364. DOI: 10.1134/S1063776106020166.
  15. Isaeva OB, Jalnine AY, Kuznetsov SP. Arnold’s cat map dynamics in a system of coupled nonautonomous van der Pol oscillators. Phys. Rev. E. 2006;74(4):046207. DOI: 10.1103/PhysRevE.74.046207.
  16. Kuznetsov SP, Pikovsky A. Autonomous coupled oscillators with hyperbolic strange attractors. Physica D. 2007;232(2):87–102. DOI: 10.1016/j.physd.2007.05.008.
  17. Kuznetsov SP, Ponomarenko VI. Realization of a strange attractor of the Smale-Williams type in a radiotechnical delay-feedback oscillator. Tech. Phys. Lett. 2008;34(9):771–773. DOI: 10.1134/S1063785008090162.
  18. Kuznetsov SP. Hyperbolic strange attractors of physically realizable systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(4):5–34 (in Russian). DOI: 10.18500/0869-6632-2009-17-4-5-34.
  19. Kuznetsov SP. Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics. Phys. Usp. 2011;54(2):119–144. DOI: 10.3367/UFNe.0181.201102a.0121.
  20. Makarenko VV. Simulation of radio electronic devices using the NI MULTISIM program. Electronic components and systems. No 1, 50–56; No 2, 51–57; No 3, 44–51; No 4, 44–51, No 6, 46–53; No 7, 54–59; No 8, 46–56; No 9, 65–69; No 12, 47–52. Kiev: VD MAIS; 2008 (in Russian).
  21. Varzarev YN, Ivantsov VV, Spiridonov BG. Simulation of Electronic Circuits in the Multisim System. Taganrog: Publishing House of TTI SFU; 2008. 81 p. (in Russian).
  22. Horowitz P, Hill W. The Art of Electronics. Vol. 1. Moscow: Mir; 1986. 510 p. (in Russian).
  23. Horowitz P, Hill W. The Art of Electronics. Vol. 2. Moscow: Mir; 1986. 592 p. (in Russian).
  24. Rempen IS, Egorov EN, Savin AN, Ponomarenko VI. Operational Amplifiers. Study Guide. Saratov: «College»; 2004. Part 1. 19 p. Part II. 16 p. (in Russian).
  25. Dmitriev AS, Panas AI. Dynamic Chaos: New Carriers Of Information For Communication Systems. Moscow: Fizmatlit; 2002. 252 p. (in Russian).
  26. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Phys. Usp. 2009;52(12):1213–1238. DOI: 10.3367/UFNe.0179.200912c.1281.
  27. Lukin KA. Noise radar technology. Telecommunications and Radio-Engineering. 2001;16(12):8.
  28. Baptista MS. Cryptography with chaos. Physics Letters A. 1998;240(1–2):50–54. DOI: 10.1016/S0375-9601(98)00086-3.
  29. Ptitsyn NV. Application of the Theory of Deterministic Chaos in Cryptography. Moscow: Bauman University Publishing; 2002. 80 p. (in Russian).
  30. Stojanovski T, Kocarev L. Chaos-based random number generators. Part I: Analysis. IEEE Trans. Circuits Syst. 2001;48(3):281–288. DOI: 10.1109/81.915385.
  31. Stojanovski T, Pihl J, Kocarev L. Chaos-based random number generators. Part II: Practical Realization. IEEE Trans. Circuits Syst. 2001;48(3):382–385. DOI: 10.1109/81.915396.
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