scholarly journals Periodic solutions for nonautonomous systems with nonsmooth quadratic or superquadratic potential

2004 ◽  
Vol 24 (2) ◽  
pp. 269 ◽  
Author(s):  
Dumitru Motreanu ◽  
Viorica V. Motreanu ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Periodic Solutions ◽  
Nonautonomous Systems ◽  
Superquadratic Potential

KNOTTED PERIODIC SOLUTIONS OF A LINEAR NONAUTONOMOUS SYSTEM AND SOME RELATED THREE-DIMENSIONAL FLOWS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250280
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Distinct Type ◽  
Frequency Parameter ◽  
Bounded Region ◽  
Nonautonomous Systems ◽  
Dimensional Phase Space

This paper considers a three-dimensional linear nonautonomous systems. It shows that for every integer frequency parameter value, this system has a distinct type of knotted periodic solutions, which lie in a bounded region of R3. Exact explicit parametric representations of the knotted periodic solutions are given. By using these parametric representations, two series of three-dimensional flows are constructed, such that these three-dimensional autonomous systems have knotted periodic orbits in the three-dimensional phase space.

scholarly journals Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Melusi Khumalo
Keyword(s):  
Numerical Methods ◽  
Periodic Solutions ◽  
Floquet Theory ◽  
Poincaré Map ◽  
Collocation Methods ◽  
Discrete Version ◽  
Qualitative Behaviour ◽  
Nonautonomous Systems ◽  
Nonautonomous Equations ◽  
Simple Systems

Nonautonomous systems with periodic solutions are encountered frequently in applications. In this paper, we will consider simple systems whose solutions are periodic with a known period. Their transformation under linearized collocation methods is investigated, using a technique called stroboscopic sampling, a discrete version of the well-known Poincaré map. It is shown that there is an inextricable relationship between AN stability (or BN stability) of the numerical methods and the correct qualitative behaviour of solutions.

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