On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach
Publication
, Journal Article
Dowell, EH; Pezeshki, C
Published in: Journal of Sound and Vibration
March 8, 1988
Many different explanations have been offered for the occurrence of chaos in Duffing's equation. Holmes has derived a criterion for the onset of chaos using Melnikov theory that is based upon the initial entanglement of the unstable manifold with the stable limit cycle. Moon offered a criterion based on physical principles by considering how much energy a trajectory had to possess to get out of the potential well of one of the stable limit cycles. In this paper, conclusive numerical evidence is offered that in order for steady state chaos to occur in this system, there must be a near intersection of the stable and unstable steady state limit cycles in the phase space of Duffing's equation. © 1988 Academic Press Limited.
Duke Scholars
Published In
Journal of Sound and Vibration
DOI
EISSN
1095-8568
ISSN
0022-460X
Publication Date
March 8, 1988
Volume
121
Issue
2
Start / End Page
195 / 200
Related Subject Headings
- Acoustics
- 51 Physical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences
Citation
APA
Chicago
ICMJE
MLA
NLM
Dowell, E. H., & Pezeshki, C. (1988). On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach. Journal of Sound and Vibration, 121(2), 195–200. https://doi.org/10.1016/S0022-460X(88)80023-3
Dowell, E. H., and C. Pezeshki. “On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach.” Journal of Sound and Vibration 121, no. 2 (March 8, 1988): 195–200. https://doi.org/10.1016/S0022-460X(88)80023-3.
Dowell EH, Pezeshki C. On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach. Journal of Sound and Vibration. 1988 Mar 8;121(2):195–200.
Dowell, E. H., and C. Pezeshki. “On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach.” Journal of Sound and Vibration, vol. 121, no. 2, Mar. 1988, pp. 195–200. Scopus, doi:10.1016/S0022-460X(88)80023-3.
Dowell EH, Pezeshki C. On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach. Journal of Sound and Vibration. 1988 Mar 8;121(2):195–200.
Published In
Journal of Sound and Vibration
DOI
EISSN
1095-8568
ISSN
0022-460X
Publication Date
March 8, 1988
Volume
121
Issue
2
Start / End Page
195 / 200
Related Subject Headings
- Acoustics
- 51 Physical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences