An algebraic criterion for the onset of chaos in nonlinear dynamical systems

Author

Ünal, A.

Author_Institution

Dept. of Mech. Eng., Santa Clara Univ., CA, USA

fYear

1988

fDate

7-9 Jun 1988

Firstpage

19

Abstract

Defines the onset of chaos in a given dynamical system and expresses the necessary and sufficient conditions as a criterion for the onset. The algebra required both in obtaining the generating power series in their shuffle product together with the two limits all can be done on a computer with a symbolic language. The following symbolic languages can be used: PL/I, REDUCE, MACSYMA, and LISP. The criterion, which is computer-algebraic, can be utilized to characterize the physical parameters´ ranges for which chaotic regimes will take place and hence can be used in designing nonlinear dynamical system to avoid such regimes

Keywords

algebra; chaos; mathematics computing; nonlinear systems; series (mathematics); symbol manipulation; LISP; MACSYMA; PL/I; REDUCE; algebraic criterion; chaos avoidance; chaotic regimes; generating power series; necessary and sufficient conditions; nonlinear dynamical systems; nonlinear system design; onset of chaos; physical parameters´ ranges; symbolic language; Algebra; Autocorrelation; Chaos; Integral equations; Laplace equations; Nonlinear dynamical systems; Nonlinear equations; Physics computing; Power generation; Transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1988., IEEE International Symposium on

Conference_Location

Espoo

Type

conf

DOI

10.1109/ISCAS.1988.14858

Filename

14858