Abstract
In the previous chapters we have introduced the methods of chaotic behaviour description. Here we will observe how the behaviour of our systems changes during the transition from periodic to chaotic states. The mechanism of the transition to chaos is of fundamental importance for understanding the phenomenon of chaotic behaviour. There are three main routes to chaos which can be observed in nonlinear oscillators.
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
Preview
Unable to display preview. Download preview PDF.
References
Newhouse, S., Ruelle, D., Takens, F. (1978): Occurrence of strange axiom A attractors near quasiperiodic flows on Tm, m 3, Commun. Math. Phys., 64, 35–40
Landau, L. D. (1944): On the problem of turbulence, C. R. Acad. Sci. URSS, 44, 311–318
Pomeau, Y., Manneville, P. (1980): Intermittent transition to turbulence in dissipative dynamical systems, Commun. Math. Phys., 74, 189–197
Sato, M., Sano, M., Sawada, Y. (1983): Universal scaling property in bifurcation structure of Duffing’s and generalized Duffing’s equations, Phys. Rev., 82A, 1654–1658
Kapitaniak, T. (1991): Chaotic Oscillations in Mechanical Systems, Manchester University Press, Manchester
Ueda, Y. (1979): Randomly transitional phenomena in the system governed by Duffing’s equation, J. Stat. Phys., 20, 181–196
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kapitaniak, T. (1998). Routes to Chaos. In: Chaos for Engineers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97719-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-97719-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63515-4
Online ISBN: 978-3-642-97719-0
eBook Packages: Springer Book Archive