Paper's Title:

Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators

Author(s):

B. Deruni¹, A. S. Hacinliyan^1,2, E. Kandiran³, A. C. Keles², S. Kaouache⁴, M.-S. Abdelouahab⁴, N.-E. Hamri⁴

¹Department of Physics,
University of Yeditepe,
Turkey.

²Department of Information Systems and Technologies,
University of Yeditepe,
Turkey

³Department of Software Development,
University of Yeditepe,
Turkey.

⁴Laboratory of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.

E-mail: berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz

Abstract:

In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.

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