On the dynamics of a periodic Colpitts oscillator forced by periodic and chaotic signals Suvra Sarkar a , Sandeepa Sarkar b , Bishnu Charan Sarkar c,⇑ a Electronics Department, Burdwan Raj College, Burdwan 713104 , WB, India b Burdwan Harisabha Hindu Girls High School (Morning), Burdwan 713104, WB, India c Physics Department, Burdwan University, Burdwan 713104, WB, India article info Article history: Received 15 July 2013 Received in revised form 4 January 2014 Accepted 4 January 2014 Available online 10 January 2014 Keywords: Chaotic Colpitts oscillator Master–slave coupling Chaos generation by bias tuning Chaotic perturbation Period doubling route abstract In this paper, we have examined effects of forcing a periodic Colpitts oscillator with peri- odic and chaotic signals for different values of coupling factors. The forcing signal is gen- erated in a master bias-tuned Colpitts oscillator having identical structure as that of the slave periodic oscillator. Numerically solving the system equations, it is observed that the slave oscillator goes to chaotic state through a period-doubling route for increasing strengths of the forcing periodic signal. For forcing with chaotic signal, the transition to chaos is observed but the route to chaos is not clearly detectable due to random variations of the forcing signal strength. The chaos produced in the slave Colpitts oscillator for a cha- otic forcing is found to be in a phase-synchronized state with the forced chaos for some val- ues of the coupling factor. We also perform a hardware experiment in the radio frequency range with prototype Colpitts oscillator circuits and the experimental observations are in agreement with the numerical simulation results. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction During last few decades, extensive studies have been done to understand the nonlinear dynamics of electronic oscillators in isolated or driven mode of oscillation [1–3]. Also coupled oscillator systems have drawn considerable attention of the researchers working in the relevant field [4–6]. A survey of recent literature reveals that, besides periodic oscillators, chaotic signal sources are also being studied both for academic interests and for their practical application potential. Chaotic signals have a few unique characterizing properties which have made it attractive in communication applications [7,8]. Moreover, chaotic dynamics of forced and coupled oscillating systems are of considerable importance in power electronics, chemical industries, biological systems and financial market related problems etc. [9,10]. As such problems related to generation and control of chaotic oscillations in common electronic systems constitute an important class in the field of nonlinear science [11–14]. In the present paper, we examine the effects of forcing a periodic electronic oscillator by an in-band periodic or chaotic signal. We have taken a Colpitts oscillator (CO) as a representative of electronic oscillators. Because, over the years, COs are very common and popular signal sources in the radio frequency (RF) and microwave frequency range for their circuit simplicity and low power requirement. Besides being used in the periodic mode, COs could be reliable sources of chaotic oscillations. Several techniques of chaotic CO design using bipolar junction transistors (BJTs) have been reported in the literature [15–17]. Novel proposals of circuit modification to overcome the limitations due to BJT transition frequencies and the synchronization phenomena of chaotic COs have been discussed by several authors [18–22]. 1007-5704/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cnsns.2014.01.004 ⇑ Corresponding author. Tel.: +91 9474041238. E-mail addresses: suvrabrc@gmail.com (S. Sarkar), sandeepaphys@gmail.com (S. Sarkar), bcsarkar_phy@yahoo.co.in (B.C. Sarkar). Commun Nonlinear Sci Numer Simulat 19 (2014) 2883–2896 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns