Chaos, Solitons and Fractals 95 (2017) 33–41 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator J. Palanivel a , K. Suresh b , S. Sabarathinam b , K. Thamilmaran b,∗ a Department of Electronics and Communication Engineering, Anjalai Ammal Mahalingam Engineering College, Koyilvenni , Tamilnadu 614403, India b Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli , Tamilnadu 620024, India a r t i c l e i n f o Article history: Received 26 September 2016 Revised 7 December 2016 Accepted 12 December 2016 Keywords: Fractional order Minimal FO Chaos Bifurcation analysis Period doubling a b s t r a c t 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 deriva- tives 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 pro- posed 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. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction Study on nonlinear dynamical systems and their complex be- havior gained a great interest among the researchers for the past few decades [1–4]. Nevertheless, it is difficult to solve the dynam- ical systems by available analytical methods. Few analytical and several numerical methods are available depending on the spe- cific situation. Especially, solving a fractional order dynamical sys- tems are more complicated [5]. The equations representing frac- tional order dynamical system involve differentiation and integra- tion of fractional order calculus. Having a history of 300 years, the fractional order calculus (FoC) was first referred by Leibniz and L’Hospital [6,7] and developed later on by many contributions. In recent years, the FoC has a variety of applications as it allows us to describe or model a real world dynamical systems more precisely than the classical integer order calculus. Studies reveal that real world dynamical systems are generally in fractional orders [8–11]. With its recent developments such as approximation method, the FoC has broadened its application area. To mention a few, physics, chemistry, engineering [12,13], electrical engineering [8,11,14], con- ∗ Corresponding author. E-mail address: maran.cnld@gmail.com (K. Thamilmaran). trol systems [9,10,15], robotics [16], signal processing [17], chemi- cal mixing [18], bio-engineering [19], electronic circuits [20,21] and mechanical oscillator [22]. Numerous studies are available on fractional order nonlinear systems [23–26]. Radwan et al. [27] studied, the stability of com- mensurate and incommensurate fractional order. A general proce- dure for studying the stability of a system with many fractional elements is also given. Ahmad et al. [28] investigated chaotic be- havior in autonomous nonlinear models of fractional order. The linear transfer function approximations of the fractional integra- tor block are calculated for a set of fractional orders, based on frequency domain arguments, and the resulting equivalent models are studied. An electronic circuit model of tree shape to realize the fractional-order operator proposed by Chen Xiang Rong et al. [29]. Jia Rong et al. [30] reported fractional-order Lorenz system. They analyzed the system using the frequency-domain approximation method and the time-domain approximation method and reported its chaotic dynamics, when the order of the fractional-order sys- tem is varied. Chao Luo Rong et al. [31] investigated a fractional- order complex Lorenz system and its dynamical behaviors. The synchronization scheme in fractional-order complex Lorenz sys- tems is also presented. Razminia Rong et al. [32] present an ac- tive control methodology for controlling the chaotic behavior of a http://dx.doi.org/10.1016/j.chaos.2016.12.007 0960-0779/© 2016 Elsevier Ltd. All rights reserved.