Four-dimensional autonomous dynamical systems with conservative flows: two-case study

Four-dimensional autonomous dynamical systems with conservative flows: two-case study Conservative chaotic systems are rare, especially autonomous smooth dynamical systems. This paper reports two four-dimensional (4D) autonomous conservative systems. The conservation of these two systems has been verified using the trace of Jacobian matrix, perpetual point theory and Hamiltonian energy theory. Numerical analyses, including phase portrait, Poincaré section, Lyapunov exponent spectrum and bifurcation diagram, verify the existence of the chaotic and quasiperiodic flows. Moreover, a electronic circuit in Multisim is built to demonstrate their chaotic dynamics, whose circuit experimental results agree well with the numerical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Four-dimensional autonomous dynamical systems with conservative flows: two-case study

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3599-6
Publisher site
See Article on Publisher Site

Abstract

Conservative chaotic systems are rare, especially autonomous smooth dynamical systems. This paper reports two four-dimensional (4D) autonomous conservative systems. The conservation of these two systems has been verified using the trace of Jacobian matrix, perpetual point theory and Hamiltonian energy theory. Numerical analyses, including phase portrait, Poincaré section, Lyapunov exponent spectrum and bifurcation diagram, verify the existence of the chaotic and quasiperiodic flows. Moreover, a electronic circuit in Multisim is built to demonstrate their chaotic dynamics, whose circuit experimental results agree well with the numerical results.

Journal

Nonlinear DynamicsSpringer Journals

Published: Jun 21, 2017

References

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