Investigation of Chaotic and Strange Nonchaotic Phenomena in Nonautonomous Wien-Bridge Oscillator with Diode Nonlinearity

Abstract

We have studied the chaotic and strange nonchaotic phenomena of a simple quasiperiodically forced Wien bridge oscillator circuit with diode as the only nonlinearity in this electronic oscillator system responsible for various nonlinear behaviors. Both the experimental results and the numerical simulation results for their confirmation are provided to show the bifurcation process. Various measures used for the numerical confirmation of SNA are power spectrum, maximal Lyapunov exponent, path of translational variables, mean square displacement, projection of poincaré section, log-log plot, and autocorrelation function. Based upon the numerical results, the birth of SNAs has been identified in the band merging route, intermittency route, and blowout bifurcation route. In addition, the birth of SNAs has been analyzed with peculiar mechanism, namely, “0-1 Test” employing the one state dynamical variable.

Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity

“…Nonlinear electronic circuits have been attracted appreciable attention in the past few years (Danca et al, 2016;Li et al, 2017;Njitacke et al, 2016;Samardzic and Zlatkovic, 2017;Senthilkumar et al, 2008;Wang et al, 2015;Wang and Xu, 2016;Zha et al, 2016). Popularly, non-autonomous circuits have attracted much research interest in nonlinear science literature owing to their simple topological structures and complex dynamics (Arulgnanam et al, 2009;Ahamed and Lakshmanan, 2013;Bao et al, 2015;Rizwana and Mohamed, 2015;Suresh et al, 2013). Until now, lots of second-and thirdorder non-autonomous circuits with various external stimuli have been proposed, within which the resultant dynamical equations are a set of nonlinear differential equations coupled with a forcing term (Ahamed and Lakshmanan, 2013;Rizwana and Mohamed, 2015;Suresh et al, 2013).…”

“…Popularly, non-autonomous circuits have attracted much research interest in nonlinear science literature owing to their simple topological structures and complex dynamics (Arulgnanam et al, 2009;Ahamed and Lakshmanan, 2013;Bao et al, 2015;Rizwana and Mohamed, 2015;Suresh et al, 2013). Until now, lots of second-and thirdorder non-autonomous circuits with various external stimuli have been proposed, within which the resultant dynamical equations are a set of nonlinear differential equations coupled with a forcing term (Ahamed and Lakshmanan, 2013;Rizwana and Mohamed, 2015;Suresh et al, 2013). Abundant dynamical behaviors including chaos, period, quasi-period, transient chaos, period-doubling and quasi-periodic routes have been revealed by numerical simulations and experimental measurements.…”

“…Abundant dynamical behaviors including chaos, period, quasi-period, transient chaos, period-doubling and quasi-periodic routes have been revealed by numerical simulations and experimental measurements. Summarily, extra nonlinearities, such as diode (Rizwana and Mohamed, 2015;Senthilkumar et al, 2008), Chua's diode (Arulgnanam et al, 2009;Suresh et al, 2013) and memristor emulator (Ahamed and Lakshmanan, 2013;Bao et al, 2015), play an important role in those nonlinear circuits. However, the Chua's diode and memristor emulator are complicated in their realization circuit topologies.…”

“…Recently, a memristive Wien-bridge oscillator is presented, which is implemented by replacing the resistor in parallel branch with a generalized memristor (Wu et al, 2015). Driven by a quasi-periodic signal, a non-autonomous Wien-bridge oscillator is proposed and its strange nonchaotic phenomenon is illustrated in Rizwana and Mohamed (2015). In these Wien-bridge oscillator-based chaotic circuits, the extra nonlinearities should be used and the operational amplifiers should be restricted to operate in linear regions, which induce that the circuit implementations have more discrete electronic components than the classical Wien-bridge oscillator.…”

A Simple Chaotic Wien Bridge Oscillator with a Fractional‐Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability

“…In a general Wien bridge oscillator, an operational amplifier is connected parallel to RC and series RC networks. An attempt is made to replace the resistor in parallel configuration with a memristor in [33][34][35] and come up with a strange nonchaotic attractor. A fractional-order memristorbased hyperchaotic Wien bridge oscillator circuit is modelled using the Adomian Decomposition method, and analysis found that compared with the integer order form, the fractional-order form revealed many intricate properties like coexisting of multiple attractors [36].…”