 OscillationsG. c. Layek ()
Chapter Chapter 5 in An Introduction to Dynamical Systems and Chaos, 2015, pp 159-202 from Springer Abstract: Abstract It is well known that some important properties of nonlinear equations can be determined through qualitative analysis. The general theory and solution methods for linear equations are highly developed in mathematics, whereas a very little is known about nonlinear equations. Linearization of a nonlinear system does not provide the actual solution behaviors of the original nonlinear system. Nonlinear systems have interesting solution features. It is a general curiosity to know in what conditions an equation has periodic or bounded solutions. Systems may have solutions in which the neighboring trajectories are closed, known as limit cycleLimit cycle s. What are the conditions for the existence of such limiting solutions? In what conditions does a system have unique limit cycle? These were some questions both in theoretical and engineering interest at the beginning of twentieth century. This chapter deals with oscillatory solutions in linear and nonlinear equations, their mathematical foundations, properties, and some applications. Keywords: Limit cycleLimit Cycle; Neighboring Trajectories; Unique Stable Limit Cycle; Close Path; Successive Zeros (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-2556-0_5 Ordering information: This item can be ordered from DOI: 10.1007/978-81-322-2556-0_5 Access Statistics for this chapter More chapters in Springer Books from Springer |
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