Title :
Proving the existence of periodic solutions using global interval Newton method
Author :
Galias, Zbigniew
Author_Institution :
Dept. of Electr. Eng., Univ. of Min. & Metall., Cracow, Poland
Abstract :
In this paper we introduce the global interval Newton method and investigate the possibility of using this method for proving the existence of periodic orbits in continuous-time dynamical systems. We compare this method with a standard version of the interval Newton method. As an example we consider a simple third order electronic circuit for which we prove the existence of several unstable periodic orbits
Keywords :
Newton method; circuit analysis computing; continuous time systems; nonlinear equations; nonlinear network analysis; nonlinear systems; Chua´s circuit; continuous-time dynamical systems; global interval Newton method; periodic orbits; periodic solutions; standard version; third order electronic circuit; unstable periodic orbits; Arithmetic; Chaos; Electronic circuits; Jacobian matrices; Newton method; Nonlinear systems; Orbits; Roundoff errors; Trajectory; Wrapping;
Conference_Titel :
Circuits and Systems, 1999. ISCAS '99. Proceedings of the 1999 IEEE International Symposium on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-5471-0
DOI :
10.1109/ISCAS.1999.780153
