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Self-Oscillations and Chaotic Dynamic of a Nonlinear Controlled Nano-Oscillator

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Abstract:

This paper concerns to the self-oscillation and chaotic motions of two coupled nano-masses connected to a hard nonlinear spring with viscous damping. The system is actuated by two external control forces to drive the masses to prescribed set points following a dynamical behavior named as regular. By means of appropriate control forces and an external harmonic excitation, it is shown that it is possible to obtain different chaotic and self-oscillation behaviors. The onset of chaos is investigated throughout the Melnikov function, and the self-oscillating motion is analyzed by means of an Adronov-Poincaré-Hopf bifurcation whose stability is deduced from the sign of the first Lyapunov value. When the first Lyapunov value associated to all equilibrium points is positive, the system may be chaotic, so it is possible to obtain chaos without any external harmonic force. On the other hand, if the first Lyapunov value at an equilibrium point is negative, a weak focus appears, and thus the interaction with an external harmonic disturbance could lead to chaotic oscillations. The appearance of different chaotic dynamics are researched by means of analytic calculations and computing simulations, from which sensitive dependence, power spectral density, Lyapunov exponents, bifurcation diagrams, Poincaré sections and chaos map are determined.

Keywords: ANDRONOV-POINCARE-HOPF BIFURCATION; CHAOS; FIRST LYAPUNOV VALUE; MELNIKOV FUNCTION; SELF-OSCILLATION

Document Type: Research Article

DOI: https://doi.org/10.1166/jctn.2010.1634

Publication date: 2010-11-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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