Abstract
A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.
| Original language | English (US) |
|---|---|
| Journal | Journal of Dynamics and Differential Equations |
| DOIs | |
| State | Accepted/In press - Mar 5 2015 |
Fingerprint
Keywords
- Approximate orbits
- Chaos
- Connecting orbits
- Heteroclinic cycle
- Homoclinic orbits
ASJC Scopus subject areas
- Analysis
Cite this
A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics. / Coomes, Brian A; Kocak, Huseyin; Palmer, Kenneth J.
In: Journal of Dynamics and Differential Equations, 05.03.2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics
AU - Coomes, Brian A
AU - Kocak, Huseyin
AU - Palmer, Kenneth J.
PY - 2015/3/5
Y1 - 2015/3/5
N2 - A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.
AB - A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.
KW - Approximate orbits
KW - Chaos
KW - Connecting orbits
KW - Heteroclinic cycle
KW - Homoclinic orbits
UR - http://www.scopus.com/inward/record.url?scp=84924193035&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84924193035&partnerID=8YFLogxK
U2 - 10.1007/s10884-015-9437-y
DO - 10.1007/s10884-015-9437-y
M3 - Article
AN - SCOPUS:84924193035
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
ER -