Abstract
In this chapter, a novel mathematical analysis for predicting master-slave chaotic synchronization is presented. In most situations when examining this type of synchronization one considers the asymptotic stability of the particular system via Lyapunov’s direct method, or conditional Lyapunov exponents are considered. Initially, in this chapter, Lyapunov’s direct method is used to show the asymptotic stability within the simplest piecewise linear master-slave chaotic flow. However, primarily the master-slave synchronization properties of the simplest quadratic chaotic flow and Ueda chaotic system are examined directly by means of mathematical manipulation of their dynamical equations, where possible, as well as via numerical simulations. In order to achieve this, numerical simulations and theoretical analysis are made use of in conjunction. In this way, it is shown that the synchronization error of the two aforementioned chaotic master-slave systems can indeed be predicted for certain driving signals, without the need for either analytical or numerical evaluation of the conditional Lyapunov exponents or employment of Lyapunov’s direct method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Physical Review Letters 64(8), 821–824 (1990)
Pecora, L.M., Carroll, T.L.: Driving systems with chaotic signals. Physical Review A 44(4), 2374–2383 (1991)
He, R., Vaidya, P.G.: Analysis and synthesis of synchronous periodic and chaotic systems. Physical Review A 46(12), 7387–7392 (1992)
Rouche, N., Habets, P., Laloy, M.: Stability Theory by Liapunov’s Direct Method, pp. 30–31. Springer, Heidelberg (1977)
Murali, K., Lakshmanan, M.: Transmission of signals by synchronization in a chaotic Van der Pol-Duffing oscillator. Physical Review E, Rapid Communications 48(3), R1624–R1626 (1993)
Sprott, J.C.: Chaos and Time-Series Analysis, pp. 230–440. Oxford University Press, Oxford (2003)
Jovic, B., Berber, S., Unsworth, C.P.: A novel mathematical analysis for predicting master – slave synchronization for the simplest quadratic chaotic flow and Ueda chaotic system with application to communications. Physica D 213(1), 31–50 (2006)
Chua, L.O., Itoh, M., Kocarev, L., Eckert, K.: Chaos synchronization in Chua’s circuit. Journal of Circuits, Systems and Computers 3(1), 93–108 (1993)
Moon, F.C.: Chaotic Vibrations - An Introduction for Applied Scientists and Engineers, pp. 24–36. Wiley Interscience, New York (1987)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jovic, B. (2011). A Novel Mathematical Analysis for Predicting Master-Slave Chaotic Synchronization. In: Synchronization Techniques for Chaotic Communication Systems. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21849-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-21849-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21848-4
Online ISBN: 978-3-642-21849-1
eBook Packages: EngineeringEngineering (R0)