Applicability of 0-1 test for strange nonchaotic attractors

Gopal, R.; Venkatesan, A.; Lakshmanan, M.

doi:10.1063/1.4808254

Cited by 57 publications

(54 citation statements)

References 55 publications

(96 reference statements)

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“…If the frequency of second harmonic force and driving force are incommensurate, then their ratio will be irrational and one can find the occurence of SNA [39][40][41][42]. On the other hand, an optimal amplitude of the high-frequency second harmonic force enhances the response of a nonlinear non-autonomous system to a low-frequency first harmonic signal.…”

Section: Introductionmentioning

confidence: 95%

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

Venkatesh

Venkatesan

2016

Pramana - J Phys

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Additional sinusoidal and different non-sinusoidal periodic perturbations applied to the periodically forced nonlinear oscillators decide the maintainance or inhibitance of chaos. It is observed that the weak amplitude of the sinusoidal force without phase is sufficient to inhibit chaos rather than the other non-sinusoidal forces and sinusoidal force with phase. Apart from sinusoidal force without phase, i.e., from various non-sinusoidal forces and sinusoidal force with phase, square force seems to be an effective weak perturbation to suppress chaos. The effectiveness of weak perturbation for suppressing chaos is understood with the total power average of the external forces applied to the system. In any chaotic system, the total power average of the external forces is constant and is different for different nonlinear systems. This total power average decides the nature of the force to suppress chaos in the sense of weak perturbation. This has been a universal phenomenon for all the chaotic non-autonomous systems. The results are confirmed by Melnikov method and numerical analysis. With the help of the total power average technique, one can say whether the chaos in that nonlinear system is to be supppressed or not.

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Section: Introductionmentioning

confidence: 95%

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

Venkatesh

Venkatesan

2016

Pramana - J Phys

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“…The 0-1 test for chaos takes as input a time series of measurements and returns a single scalar value of either 0 for periodic attractors or 1 for chaotic attractors [31,34]. According to [35] value of (K c ) can be obtained from: …”

Section: Dynamic Analysis Of a Fractional-ordermentioning

confidence: 99%

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

Balthazar

Brasil

Félix

et al. 2016

J. Phys.: Conf. Ser.

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Abstract. This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015. IntroductionThis paper shows a series of problems related to nonlinear dynamics and control, correlated to Electromechanical Systems [1] using an elastic support. Here, we analyzed such systems those fall into three groups: the conventional MACRO, MEMS and NEMS electro-mechanical systems, taking into account the existence of a full interaction between mechanical and electrical field quantities. The aim of this paper is to describe a large number of phenomena caused by the action of vibrations on nonlinear electro-mechanical systems and the energy source supply to it. This paper gives a general description of this class of phenomena which has been discussed in recent years.

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“…The 0-1 test for chaos takes as input a time series of measurements and returns a single scalar value of either 0 for periodic attractors or 1 for chaotic attractors [9]. According to [9] the value of c K is given by:…”

Section: System Description and Governing Equationsmentioning

confidence: 99%

“…For the numerical simulations, we used the following dimensionless parameters: μ we applied the 0-1 test to verify chaotic behaviour of the system, as detailed in [9]. The 0-1 test for chaos takes as input a time series of measurements and returns a single scalar value of either 0 for periodic attractors or 1 for chaotic attractors [9].…”

Section: System Description and Governing Equationsmentioning

confidence: 99%

On nonlinear dynamics and control of a robotic arm with chaos

Félix

Silva

Balthazar

et al. 2014

MATEC Web of Conferences

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Abstract. In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC) and the optimal linear feedback control (OLFC). The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC) is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC) involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

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Applicability of 0-1 test for strange nonchaotic attractors

Cited by 57 publications

References 55 publications

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

On nonlinear dynamics and control of a robotic arm with chaos

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