Abstract
A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.
| Original language | English |
|---|---|
| Pages (from-to) | 509-518 |
| Number of pages | 10 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 20 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Feb 2010 |
| Externally published | Yes |
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Keywords
- Analytical solutions
- Nonautonomous systems
- Piecewise linear systems
ASJC Scopus subject areas
- General
- Engineering(all)
- Applied Mathematics
- Modelling and Simulation
Cite this
Analytical solutions of systems with piecewise linear dynamics. / Kominis, Y.; Bountis, T.
In: International Journal of Bifurcation and Chaos, Vol. 20, No. 2, 02.2010, p. 509-518.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analytical solutions of systems with piecewise linear dynamics
AU - Kominis, Y.
AU - Bountis, T.
PY - 2010/2
Y1 - 2010/2
N2 - A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.
AB - A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.
KW - Analytical solutions
KW - Nonautonomous systems
KW - Piecewise linear systems
UR - http://www.scopus.com/inward/record.url?scp=77951606809&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77951606809&partnerID=8YFLogxK
U2 - 10.1142/S0218127410025570
DO - 10.1142/S0218127410025570
M3 - Article
VL - 20
SP - 509
EP - 518
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 2
ER -