Characterization of Chaotic Behavior in Nonlinear Vibration Systems. (Applications of the Methods of Statistical Mechanics without System Equations).

The complex dynamics of a pendulum controlled by a Proportional-Derivative (PD) compensator are analyzed. A classification of equilibrium points and the characterization of their bifurcations is also presented. It is shown that the controlled pendulum may exhibit a chaotic behavior when the desired position is periodic and the proportional gain and total dissipation are small enough.

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Characterization of a Strongly Nonlinear Vibration Absorber for Aerospace Applications

Topics in Nonlinear Dynamics, Volume 3 - Conference Proceedings of the Society for Experimental Mechanics Series ◽

10.1007/978-1-4614-2416-1_15 ◽

2012 ◽

pp. 199-207

Author(s):

Sean A. Hubbard ◽

Timothy J. Copeland ◽

D. Michael McFarland ◽

Lawrence A. Bergman ◽

Alexander F. Vakakis

Keyword(s):

Nonlinear Vibration ◽

Vibration Absorber ◽

Nonlinear Vibration Absorber ◽

Strongly Nonlinear ◽

Aerospace Applications

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Thermal Dynamics for Characterizing Nonlinear Circuit Behavior

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420300104 ◽

2020 ◽

Vol 30 (05) ◽

pp. 2030010

Author(s):

Arturo Buscarino ◽

Carlo Famoso ◽

Luigi Fortuna ◽

Mattia Frasca ◽

Luca Patanè

Keyword(s):

Linear Growth ◽

Chaotic Behavior ◽

Control Strategies ◽

Thermal Characterization ◽

Operating Regime ◽

Electronic Circuits ◽

Thermal Dynamics ◽

Thermal Transients ◽

Dynamical Regimes

In this paper, we focus on the thermal characterization of nonlinear electronic circuits deriving some conditions which suggest the existence of a relationship with the specific dynamic behavior shown by the circuit. A series of thermographic experiments indicate that the chaotic behavior in electronic circuits is associated with slower thermal transients, a slow linear growth of the temperature during the normal operating regime and lower overall temperature increase with respect to other dynamical regimes. Three experimental case studies are reported and discussed, considering also the effect of chaos control strategies.

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CHARACTERIZATION OF CHAOTICITY IN THE TRANSIENT CURRENT THROUGH PMMA THIN FILMS

Fractals ◽

10.1142/s0218348x0600309x ◽

2006 ◽

Vol 14 (02) ◽

pp. 125-131 ◽

Cited By ~ 4

Author(s):

A. HACINLIYAN ◽

Y. SKARLATOS ◽

H. A. YILDIRIM ◽

G. SAHIN

Keyword(s):

Thin Films ◽

Time Series ◽

Lyapunov Exponent ◽

Power Law ◽

Chaotic Behavior ◽

Transient Current ◽

Positive Lyapunov Exponent ◽

Aluminum Films ◽

Thin Aluminum

Chaotic behavior in the transient current through thin Aluminum-PMMA-Aluminum films has been analyzed for times ranging up to 30,000s, in the temperature range 293–363K for applied voltages in the range 10–80V. Time series analysis reveals a positive Lyapunov exponent consistently and reproducibly throughout this range. Power law relaxation as reflected by the autocorrelation function and the positive Lyapunov exponent show parallel behaviors as a function of applied electric field.

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