DocumentCode
571225
Title
Chaotic solutions of a differential equation with piecewise linearity
Author
Lu, Chunqing
Author_Institution
Dept. of Math. & Stat., Southern Illinois Univ. Edwardsville, Edwardsville, IL, USA
fYear
2012
fDate
6-11 Aug. 2012
Firstpage
117
Lastpage
120
Abstract
The paper studies a second order nonlinear differential equation whose right hand side is a piecewise linear function. It proves the coexistence of a countably set of periodic solutions and an uncountable set of bounded non-periodic solutions. The Weierstrass approximation theorem is applied so that the piecewise linear function can be approximated by a polynomial on the finite interval. The result can be also used to explain the chaos on some smooth nonlinear dynamical systems.
Keywords
chaos; nonlinear differential equations; nonlinear dynamical systems; piecewise linear techniques; Weierstrass approximation theorem; bounded nonperiodic solutions; chaotic solutions; nonlinear dynamical systems; piecewise linear function; piecewise linearity; second order nonlinear differential equation; Approximation methods; Chaos; Differential equations; Mathematical model; Piecewise linear approximation; Polynomials;
fLanguage
English
Publisher
ieee
Conference_Titel
Nonlinear Science and Complexity (NSC), 2012 IEEE 4th International Conference on
Conference_Location
Budapest
Print_ISBN
978-1-4673-2702-2
Electronic_ISBN
978-1-4673-2701-5
Type
conf
DOI
10.1109/NSC.2012.6304738
Filename
6304738
Link To Document