Calculation of the isocline for the fixed point with a specified argument of complex multipliers

Author

Ueta, Tetsushi ; Tsuji, Shigeki ; Yoshinaga, Tetsuya ; Kawakami, Hiroshi

Author_Institution

Fac. of Eng., Tokushima Univ., Japan

Volume

3

fYear

2001

fDate

6-9 May 2001

Firstpage

755

Abstract

This paper proposes a calculation method to obtain the location of the fixed point in given nonlinear discrete system when the argument of complex multipliers is specified. We can calculate an isocline corresponding to the specified argument, then the stability and instantaneous phase around the fixed point can be discussed. As an application, we also propose a new calculation method of NS bifurcation parameter values with the specified argument. In addition, cross points of a cusp in a periodic entrainment region and the NS bifurcation curve is identified by this application

Keywords

bifurcation; discrete systems; nonlinear dynamical systems; stability; Neimark-Sacker bifurcation; complex multiplier argument; cross point; cusp; fixed point; instantaneous phase; isocline; nonlinear discrete system; periodic entrainment; stability; Artificial intelligence; Bifurcation; Chaos; Electric breakdown; Equations; Frequency; Jacobian matrices; Newton method; Stability; Tongue;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on

Conference_Location

Sydney, NSW

Print_ISBN

0-7803-6685-9

Type

conf

DOI

10.1109/ISCAS.2001.921442

Filename

921442