International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.3, Jun. 2015, Pub. Date: Apr. 22, 2015
Unusual Frequency Distribution Function Shape Generated by Particles Making Brownian Walk Along Line With Monotone Increasing Friction
Pages: 91-97 Views: 1523 Downloads: 677
[01] Vladimir A. Dobrynskii, Institute for Metal Physics of N. A. S. U., Kiev, Ukraine.
With aid of computer simulation it is studied a 1-dimensional frequency distribution function of the particles which make forced oscillations along the y-axis and noise-excited Brownian walks along the x-axis on the plane exhibiting spatially non-linear non-homogeneous friction. The particle oscillations and their Brownian walks appear due to a joint action both of simple harmonic (sinusoidal) force and impulse noise. It is stated that the frequency distribution function depends very much on the starting point that the particles begin their movement and the given point position variation changes its form sometimes so much that its different visible shapes look as the ones of absolutely different frequency distribution functions which do yield by means of distinctly different ordinary differential equation systems. Thus we reveal a phenomenon of visible “disintegration” of the one-peak frequency distribution function into the two-peak one having the deepest pit between the peaks.
Frequency Distribution Function, Brownian Particle Walk, Impulse Noise
[01] Haken H. Synergetics. Springer. Berlin, 1983.
[02] Haken H. Advanced synergetics. Springer. Berlin, 1985.
[03] Zaslavsky G.M., Sagdeev R.Z., Usikov D.A. and Chernikov A.A. Weak chaos and quasi-regular patterns. Cambridge University Press. Cambridge, 1987.
[04] Rěvěsz P. Random walk in random and non-random environments. World Scientific. Singapore, 1990.
[05] Protter P. Stochastic integration and differential equations. Springer. Berlin, 1992.
[06] Schuster H.G. Deterministic Chaos. Springer. 3rd edition. Berlin, 1995.
[07] Karatzas I. and Shreve S.E. Brownian motion and stochastic calculus, Springer. 2nd edition. Berlin, 1996.
[08] Vavrin D.M., Ryabov V.B., Sharapov S.A. and Ito H.M. Chaotic states of weakly and strongly nonlinear oscillators with quasiperiodic excitation. Phys. Rev E 53, 1996, pp. 103-114.
[09] Rodrigues R. and Tuckwell H. Statistical properties of stochastic nonlinear dynamical models of single spiking newrons and newral networks. Phys. Rev E 54, 1996, pp. 5585-5590.
[10] Lücking H. Pathological tremors: Deterministic chaos or nonlinear oscillators? Chaos 10(1), 2000, pp. 278-288.
[11] Gus S.A. and Sviridov M.V. “Green” noise in quasi-stationary stochastic systems. Chaos 11(3), 2001, pp. 605-610.
[12] Higham D. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review 43, 2001, pp. 525-546.
[13] Wang X. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 2002, pp. 1-20.
[14] Ivanov M.A, Dobrynskiy V.A. Random walk of oscillator on the plane with non-homogeneous friction. Int. INFA-ANS J. Problems Nonlinear Analysis in Engineering Systems”, vol. 12, no. 1(15), 2006, pp. 101-116.
[15] Ivanov M.A, Dobrynskiy V.A. Stochastic dynamics of oscillator drift in media with spatially non-homogeneous friction, J. Automation and Information Sci., vol. 40., no. 7, 2008, pp. 9-25.
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