q-thermostatistics of noise-driven Van der Pol oscillator

Deniz Eroglu, Meltem Ozkan and G. Baris Bagci

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 8, 1417-1423

Abstract: We study the noise-driven Van der Pol oscillator whose dissipative term yields stationary distributions of the q-exponential form. The thermostatistical observables such as internal energy and temperature are also calculated. Since this model depends on a control parameter which acts as a coupling parameter between the system and environment, the noise-driven Van der Pol oscillator also serves as a nice model where the interplay of both nonextensivity and open character of the system can be considered. We observe that the model behaves as if it is coupled to a finite heat bath for small values of control parameter. As the control parameter increases, the effect of the linear friction coefficient disappears, and the stationary distribution becomes a q-Gaussian, thereby breaking the coupling with the finite heat bath. Finally, we remark that negative temperature values are not observed contrary to an earlier analysis of a similar model. The elucidation of this point is commented in the framework of the misidentification of the correct form of the q-exponentials and the nonextensivity index q.

Keywords: q-thermostatistics; Nonextensivity; Stationary states; Van der Pol model; External noise (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:8:p:1417-1423

DOI: 10.1016/j.physa.2010.12.013

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