Hyperbolic chaotic attractor in amplitude dynamics of coupled self-oscillators with periodic parameter modulation

In this paper, we study effects of the secondary bifurcations in the neighborhood of the primary codimension-two bifurcation point. The twin-well potential Duffing oscillator is considered and the investigations are focused on the new scenario of destruction of the cross-well chaotic attractor. The phenomenon belongs to the category of the subduction scenario and relies on the replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. The exploration of a sequence of accompanying bifurcations throws more light on the complex phenomena that may occur in the neighborhood of the primary codimension-two bifurcation point. It shows that in the close vicinity of the point there appears a transition zone in the system parameter plane, the zone which separates the two so-far investigated scenarios of annihilation of the cross-well chaotic attractor.

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Observation of Chaotic Attractor in Spatially Extended Systems: Coarse-Grained Dimension of Frozen Chaos

Japanese Journal of Applied Physics ◽

10.1143/jjap.38.3784 ◽

1999 ◽

Vol 38 (Part 1, No. 6A) ◽

pp. 3784-3792

Author(s):

Donghak Choi ◽

Nobuko Fuchikami ◽

Eriko Hirokami ◽

Shunya Ishioka ◽

Masayoshi Naito

Keyword(s):

Chaotic Attractor ◽

Coarse Grained ◽

Extended Systems ◽

Spatially Extended ◽

Spatially Extended Systems

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Suppressing large excursions to a chaotic attractor using occasional feedback control

Physical Review E ◽

10.1103/physreve.54.r1036 ◽

1996 ◽

Vol 54 (2) ◽

pp. R1036-R1039 ◽

Cited By ~ 5

Author(s):

P. Parmananda ◽

M. Eiswirth

Keyword(s):

Feedback Control ◽

Chaotic Attractor

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Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

10.21203/rs.3.rs-263593/v1 ◽

2021 ◽

Author(s):

Ali Durdu ◽

Yılmaz Uyaroğlu

Keyword(s):

Active Control ◽

Fractional Order ◽

Chaotic Attractor ◽

Secure Communication ◽

Chaotic Systems ◽

Control Method ◽

Initial Conditions ◽

Data Communication ◽

Experimental Results ◽

Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

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