Abstract
In this chapter, the theory of dynamical system synchronization will be applied to the function synchronization of two distinct dynamical systems. Periodic and chaotic synchronizations between two distinct dynamical systems under specific constraints will be investigated. The analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator will be presented, and the invariant domain of sinusoidal synchronization will be discussed. From analytical conditions, the control parameter map will be developed. The function synchronization identification of two distinct dynamical systems with specific constraints must be carried out only by G-functions. The significance of the function synchronization of distinct dynamical systems is to make the synchronicity behaviors hidden, which can be very useful for telecommunication synchronization and network security.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Luo ACJ (2008) A theory for flow switchability in discontinuous dynamical systems. Nonlinear Anal Hybrid Syst 2(4):1030–1061
Luo ACJ (2009) A theory for synchronization of dynamical systems. Commun Nonlinear Sci Numer Simul 14:1901–1951
Luo ACJ (2008) Global tangency and transversality of periodic flows and chaos in a periodically forced, damped Duffing oscillator. Int J Bifurcat Chaos 18:1–40
Luo ACJ, Han PS (2000) The dynamics of resonant and stochastic layers in a periodically-driven pendulum. Chaos Solitons Fractals 11:2349–2359
Min FH, Luo ACJ (2012) Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints. Chaos Solitons Fractals 45:998–1011
Min FH, Luo ACJ (2012) Synchronization of a controlled, noised, gyroscope system with an expected gyroscope system. J Nonlinear Syst Appl 3:1–9
Min FH, Luo ACJ (2011) Sinusoidal synchronizations of the Duffing oscillator with a chaotic pendulum. Phys Lett A 375:3080–3089
Luo ACJ, Min FH (2011) Synchronization of a periodically forced Duffing oscillator with a periodically excited pendulum. Nonlinear Anal Real World Appl 12:1810–1827
Luo ACJ, Min FH (2011) The mechanism of a controlled pendulum synchronizing with periodic motions in a periodically forced, damped Duffing oscillator. Int J Bifurcat Chaos 21:1813–1829
Luo ACJ, Min FH (2011) The chaotic synchronization of a controlled pendulum with a periodically forced, damped Duffing oscillator. Commun Nonlinear Sci Numer Simul 16:4704–4717
Luo ACJ, Min FH (2011) Synchronization dynamics of two different dynamical systems. Chaos Solitons Fractals 44:362–380
Min FH, Luo ACJ (2012) On parameter characteristics of chaotic synchronization in two nonlinear gyroscope systems. Nonlinear Dyn 69:1203–1223
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Luo, A.C.J. (2013). Function Synchronizations. In: Dynamical System Synchronization. Nonlinear Systems and Complexity, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5097-9_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5097-9_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5096-2
Online ISBN: 978-1-4614-5097-9
eBook Packages: EngineeringEngineering (R0)