Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

Thamilmaran, K.; Senthilkumar, D. V.; Venkatesan, A.; Lakshmanan, M.

doi:10.1103/physreve.74.036205

Cited by 62 publications

(42 citation statements)

References 48 publications

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“…Type-I intermitttency route to SNA was reported in a quasiperiodically forced series LCR circuit by Venkatesan et al [31]. Recently, three prominent routes, namely HeagyHammel, fractalization and type-II intermittency routes to SNAs have been identified and reported in a quasiperiodically forced negative conductance series LCR circuit with diode as the nonlinear element [32]. The birth of strange nonchaotic attractors through formation and merging of bubbles in a quasiperiodically forced Chua's oscillator was studied very recently by Suresh et al [37].…”

Section: Introductionmentioning

confidence: 95%

“…Following the pioneering work of Grebogi et al [4], SNAs have been extensively investigated numerically in dynamical systems, such as biological oscillators [5,6], driven Duffing type oscillators [7][8][9][10][11] and in certain maps, namely driven velocitydependent systems [12,13], two dimensional maps [14], quasiperiodically forced logistic map [15][16][17][18][19][20], one dimensional cubic map [21][22][23][24], Harper map [25], map representing driven damped superconducting quantum interference device [26][27][28] and SNAs in HH-neural oscillator [29]. In some physically relevant situations, the existence of SNAs have also been demonstrated experimentally such as in electronic circuits [30][31][32][33], in neon glow discharge experiment [34] and in quasiperiodically forced, buckled, magnetoelastic ribbon [35]. Different routes to SNAs and different scenarios for the formation of SNAs along with their distinct signatures/mechanisms have been summarized in references [33] and [36].…”

Section: Introductionmentioning

confidence: 99%

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Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element

Arulgnanam¹,

Prasad

Thamilmaran

et al. 2015

Int. J. Dynam. Control

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A new route to strange nonchaotic attractors (SNAs), known as multilayered bubble route to SNA, has been identified in a quasiperiodically forced series LCR circuit with a simple nonlinear element. Upon increasing the control parameter, the stable orbits of the torus become unstable, which induces formation of bubbles in the neighbourhood of the resonating region of the torus. We have observed three tori with three smooth branches in the Poincaré map which gradually loose their smoothness and ultimately approach bubble formation, and then approach fractal behaviour via SNAs before the onset of chaos. The bubbles gradually enlarge and subsequently another three layers of bubbles are formed as a function of the control parameter. The layers get increasingly wrinkled as a function of the control parameter, resulting in the creation of SNAs which are charaterized by Poincaré maps. Apart from the multilayered bubble route to SNA, Heagy-Hammel and fractalization routes to SNA have also been numerically observed and are characterized qualitatively interms of phase portraits, power spectrum. The above mentioned three routes are further characterized quantitatively, by singular-continuous spectrum analysis, phase sensitivity measure, distribution of A. Arulgnanam finite time Lyapunov exponents, largest Lyapunov exponent and its variance.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element

Arulgnanam¹,

Prasad

Thamilmaran

et al. 2015

Int. J. Dynam. Control

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“…On employing a second harmonic perturbation to a periodically driven nonlinear system to exhibit the vibrational resonance phenomenon, it has been found [21][22][23][24][25][26][27][28][29][30] that if the frequency of the second harmonic force and the driving force are incommensurate, then their ratio will be irrational and one can find the occurrence of strange nonchaotic attractors (SNAs) in these systems. Such systems are designated as quasiperiodically driven nonlinear systems (QPDNS).…”

Section: Introductionmentioning

confidence: 99%

Design and implementation of dynamic logic gates and R-S flip-flop using quasiperiodically driven Murali-Lakshmanan-Chua circuit

Venkatesh¹,

Venkatesan²,

Lakshmanan

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as 'region of signal propagation'. Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the 'region of logical operation'. Based on this region, we propose implementing the dynamic logic gates, namely AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves without altering the system parameters. Further, we show that a single QPDMLC system will produce simultaneously two outputs which are complementary to each other. As a result, a single QPDMLC system yields either AND as well as NAND or OR as well as NOR gates simultaneously. Then we combine the corresponding two QPDMLC systems in a cross-coupled way and report that its dynamics mimics that of fundamental R-S flip-flop circuit. All these phenomena have been explained with analytical solutions of the circuit equations characterizing the system and finally the results are compared with the corresponding numerical and experimental analysis. Nonlinear dynamics based computing is an emerging field which can replace silicon chips and is becoming increasingly popular in nonlinear and chaotic dynamics, and computing research. Actually, Boolean based silicon chips are extremely logical in their operations. These logical operations can be classified into two groups, namely combinational logic circuits and sequential logic circuits. The basic building blocks for combinational logic circuits are the logic gates, namely AND, OR, NOT, NAND, NOR, etc., whereas the basic building block for sequential logic circuits is the flip-flop. Here, we have proposed a new mechanism by using a quasi-periodically driven nonlinear dynamical system exhibiting a strange non-chaotic attractor for constructing the logic gates AND/NAND/OR/NOR and fundamental R-S flip-flop circuit with Murali-LakshmananChua circuit as an example. By only imposing constraints on the logic high and logic low values of the input signal, we are able to implement these dynamic logic gates and flip-flop. In fact, without altering the system parameters, we point out how the logical operations can be decided by the asymmetrical input square waves. Consequently, dynamic computing using the behaviour of nona) Electronic mail: venkatesh.sprv@gmail.com b) Electronic mail: av.phys@gmail.com c) Electronic mail: lakshman@cnld.bdu.ac.in linear dynamical systems is shown to be quite implementable in hardware devices. Our results also show that nonlinearity is more significant than the existence of chaos for design of the logic gates and latches.

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“…2 Thus far, SNAs have been studied in various nonlinear models [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and have been observed in experiments using electronic circuits, [22][23][24][25] magnetoelastic ribbons, 26 and electrochemical cells 27 (see also Refs. 28-30, and references therein).…”

Section: Introductionmentioning

confidence: 99%

Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency

Uenohara

Mitsui

Hirata

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We experimentally study strange nonchaotic attractors (SNAs) and chaotic attractors by using a nonlinear integrated circuit driven by a quasiperiodic input signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. It is a difficult problem to distinguish between SNAs and chaotic attractors experimentally. If a system has an SNA as a unique attractor, the system produces an identical response to a repeated quasiperiodic signal, regardless of the initial conditions, after a certain transient time. Such reproducibility of response outputs is called consistency. On the other hand, if the attractor is chaotic, the consistency is low owing to the sensitive dependence on initial conditions. In this paper, we analyze the experimental data for distinguishing between SNAs and chaotic attractors on the basis of the consistency. Strange nonchaotic attractors (SNAs) often appear in dynamical systems driven by a quasiperiodic signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. In fact, typical orbits are insensitive to initial conditions under a common quasiperiodic signal. Owing to their characteristics reminiscent of both quasiperiodic order and chaos, SNAs have attracted the attention of researchers from both theoretical and experimental perspectives. Conventionally, the information dimension is often employed to distinguish between SNAs and chaotic attractors in experiments. However, using the information dimension for the experimental distinction between these types of attractors is difficult as the estimation of the information dimension is highly sensitive to noise, and requires rather long time series. Recently, Ngamga et al. 1 proposed a method for distinguishing between SNAs and chaotic attractors, which utilizes the consistency property of SNAs. Consistency here means that a nonlinear system shows the same response to the same input signal after some transient time, regardless of the initial conditions. In the method proposed by Ngamga et al., the determinism for a cross-recurrence plot of two response time series to the same input signal is used as a consistency measure. However, to our knowledge, there is no research paper on using their cross-recurrence method to experimentally distinguish between SNAs and chaotic attractors. In this study, we evaluated the consistency of a system by using the zero-delay normalized cross-correlation and Ngamga et al.'s cross-recurrence methods. By combining spectrum analysis and evaluation of consistency, we showed that SNAs and chaotic attractors can be distinguished more precisely as compared to conventional methods.

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Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

Cited by 62 publications

References 48 publications

Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element

Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element

Design and implementation of dynamic logic gates and R-S flip-flop using quasiperiodically driven Murali-Lakshmanan-Chua circuit

Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency

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