Abstract
To introduce first-order ODEs in three variables.
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
Bibliography
N. Arnold, Chemical Chaos, Hippo, London, 1997.
J. Borresen and S. Lynch. Further investigation of hysteresis in Chua’s circuit, Int. J. Bifurcation and Chaos, 12 (2002), 129–134.
A. Buscarino, L. Fotuna, M. Frasca and G. Sciuto A Concise Guide to Chaotic Electronic Circuits, Springer, New York, 2014.
J.P. Eckmann, S.O. Kamphorst, D. Ruelle and S. Ciliberto, Lyapunov exponents from time series, Physical Review A, 34(6) (1986), 4971–4979.
S. Ellner and P. Turchin, Chaos in a noisy world - new methods and evidence from time-series analysis, American Naturalist 145(3) (1995), 343–375.
R. Field and M. Burger, eds., Oscillations and Travelling Waves in Chemical Systems, Wiley, New York, 1985.
K. Geist, U. Parlitz and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Progress of Theoretical Physics, 83-5 (1990), 875–893.
G.A. Gottwald and I.Melbourne, A new test for chaos in deterministic systems, Proc. Roy. Soc. Lond. A, 460-2042 (2004), 603–611.
R.C. Hilborn, Chaos and Nonlinear Dynamics - An Introduction for Scientists and Engineers, Oxford University Press, Second ed., Oxford, UK, 2000.
B. Krauskopf, H.M. Osinga, E.J. Doedel, M.E. Henderson, J.M. Guckenheimer, A. Vladimirsky, M. Dellnitz and O. Junge, A survey of methods for computing (un)stable manifolds of vector fields, Int. J. Bifurcation and Chaos 15(3) (2005), 763–791.
Lorenz E.N. Deterministic non-periodic flow, J. Atmos. Sci., 20 (1963), 130–141.
R.N. Madan, Chua’s Circuit: A Paradigm for Chaos, Singapore, World Scientific, 1993.
A. Pikovsky and A. Politi, Lyapunov Exponents: A Tool to Explore Complex Dynamics, Cambridge University Press, Cambridge, 2016.
M.T. Rosenstein, J.J. Collins and C.J. Deluca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65 (1–2), (1993), 117–134.
O.E. Rössler, An equation for continuous chaos, Phys. Lett., 57-A (1976), 397–398.
S.K. Scott, Oscillations, Waves, and Chaos in Chemical Kinetics, Oxford Science Publications, Oxford, UK, 1994.
C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer-Verlag, New York, 1982.
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed., Springer-Verlag, New York, 2003.
A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16, (1985), 285–317.
P. Zhou, X.H. Luo and H.Y. Chen, A new chaotic circuit and its experimental results, Acta Physica Sinica 54(11), (2005), 5048–5052.
M. Zoltowski, An adaptive reconstruction of chaotic attractors out of their single trajectories, Signal Process., 80(6) (2000), 1099–1113.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Lynch, S. (2017). Three-Dimensional Autonomous Systems and Chaos. In: Dynamical Systems with Applications Using Mathematica®. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61485-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-61485-4_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-61484-7
Online ISBN: 978-3-319-61485-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)