Title :
Chaotic solutions of a differential equation with piecewise linearity
Author_Institution :
Dept. of Math. & Stat., Southern Illinois Univ. Edwardsville, Edwardsville, IL, USA
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;
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
DOI :
10.1109/NSC.2012.6304738
