Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator. (February 2017)

• Record Type: Journal Article
• Authors: Palanivel, J.; Suresh, K.; Sabarathinam, S.; Thamilmaran, K.
• Is Part Of: Chaos, solitons and fractals. Volume 95(2017)
• Page Start: 33
• Page End: 41
• Publication Date: 2017-02
• Subjects: Fractional order -- Minimal FO -- Chaos -- Bifurcation analysis -- Period doubling; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.12.007
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The lowest fractional order is identified in a nonautonomous system and confirmed through numerical and experimental investigations. The analogue electronic circuit constructed for fractional order forced LCR circuit.3. The movement of bifurcation point are analyzed in detail. The stability condition for lowest order is evaluated. Abstract: We report the dynamics of a low dimensional fractional order forced LCR circuit using Chua's diode. The stability analysis is performed for each segment of the piecewise linear curve of Chua's diode and the conditions for the oscillation and double scroll chaos are obtained. The effect of fractional order on the bifurcation points are studied with the help of bifurcation diagrams. We consider both the derivatives of the systems current and voltage as fractional derivatives. When the order of the derivatives is decreased, the system exhibits interesting dynamical behavior. For instance, the value of the fractional order corresponding to the voltage is decreased, the chaotic regime in the system decreases. But in the case of current, the chaotic regime in the system increases initially and beyond a certain value of order, the chaotic regime decreases and extinguishes from the system. We found the lowest order for exhibiting chaos in the fractional order of the circuit as 2.1. For the first time, the experimental analogue of our proposed system is made by using the frequency domain approximation. The results are obtained from the experimental observations are compared with numerical simulations and found that they match closely with each other. The existence of chaos in the circuit is analyzed with the help of 0-1 test and power spectrum.