DocumentCode :
2264932
Title :
Bifurcation and chaos in the fractional Chua and Chen systems with very low order
Author :
Cafagna, Donato ; Grassi, Giuseppe
Author_Institution :
Dipt. Ing. Innovazione, Univ. del Salento, Lecce, Italy
fYear :
2009
fDate :
24-27 May 2009
Firstpage :
2846
Lastpage :
2849
Abstract :
The aim of this work is to analyze the chaotic behaviors in the fractional-order Chua and Chen systems via a time-domain approach. The objective is achieved using a decomposition method, which allows the solution of the fractional differential equations to be written in closed form. Specifically, by taking advantage of the capabilities given by time-domain analysis, the paper illustrates three remarkable findings: i) chaos exists in the fractional Chua system with very low order, that is, 0.03, which represents the lowest order reported in literature for any dynamical system studied so far; ii) chaos exists in the fractional Chen system with order as low as 0.24, which represents the smallest value reported in literature for the Chen system; iii) it is feasible to show the occurrence of pitchfork bifurcations and period-doubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.
Keywords :
Chua´s circuit; bifurcation; chaos; differential equations; time-domain analysis; decomposition method; dynamical system; fractional differential equations; fractional order Chua-Chen systems; period-doubling routes; time-domain analysis; Bifurcation; Chaos; Differential equations; Fractional calculus; Frequency; Nonlinear dynamical systems; Time domain analysis;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Circuits and Systems, 2009. ISCAS 2009. IEEE International Symposium on
Conference_Location :
Taipei
Print_ISBN :
978-1-4244-3827-3
Electronic_ISBN :
978-1-4244-3828-0
Type :
conf
DOI :
10.1109/ISCAS.2009.5118395
Filename :
5118395
Link To Document :
بازگشت