0
Technical Brief

General Noise-Perturbed Superior Julia Sets

[+] Author and Article Information
Mamta Rani

Department of Computer Applications,
Krishna Engineering College,
95, Loni Road, Mohan Nagar,
Ghaziabad 201007, UP, India
e-mail: mamtarsingh@rediffmail.com

Rashi Agarwal

Department of Information Technology,
Sharda University,
Knowledge Park II,
Greater Noida 201306, UP, India
e-mail: rasagarwal@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 13, 2011; final manuscript received June 16, 2011; published online July 23, 2012. Assoc. Editor: Eric A. Butcher.

J. Comput. Nonlinear Dynam 8(2), 024501 (Jul 23, 2012) (4 pages) Paper No: CND-11-1007; doi: 10.1115/1.4006785 History: Received January 13, 2011; Revised June 16, 2011

The aim of this paper is to offer an integrated approach to study the additive and multiplicative noises with respect to perturbations in superior Julia sets. External and internal perturbations in superior Julia sets are analyzed under the mixed effect of additive and multiplicative noises.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Topics: Noise (Sound)
Your Session has timed out. Please sign back in to continue.

References

Rani, M., and Kumar, V., 2004, “Superior Julia Set,” J. Korea Soc. Math. Educ. Ser. D: Res. Math. Educ., 8(4), pp. 261–277. [CrossRef]
Rani, M., and Kumar, V., 2004, “Superior Mandelbrot Set,” J. Korea Soc. Math. Educ. Ser. D: Res. Math. Educ., 8(4), pp. 279–291. [CrossRef]
Kumar, M., and Rani, M., 2005, “A New Approach to Superior Julia Sets,” J. Nature Phys. Sci., 19(2), pp. 148–155, MR2744660.
Rani, M., and Agarwal, R., 2009, “Generation of Fractals from Complex Logistic Map,” Chaos, Solitons Fractals, 42(1), pp. 447–452. [CrossRef]
Argyris, J., Andreadis, I., Pavlos, G., and Athanasiou, M., 1998, “On the Influence of Noise on the Correlation Dimension of Chaotic Attractors,” Chaos, Solitons Fractals, 9(3), pp. 343–361. [CrossRef]
Argyris, J., Andreadis, I., and Karakasidis, T. E., 2000, “On Perturbation of the Mandelbrot Map,” Chaos, Solitons Fractals, 11(7), pp. 1131–1136. [CrossRef]
Argyris, J., Karakasidis, T. E., and Andreadis, I., 2000, “On the Julia Set of the Perturbed Mandelbrot Map,” Chaos, Solitons Fractals, 11(13), pp. 2067–2073. [CrossRef]
Argyris, J., Karakasidis, T. E., and Andreadis, I., 2002, “On the Julia Sets of a Noise-Perturbed Mandelbrot Map,” Chaos, Solitons Fractals, 13(2), pp. 245–252. [CrossRef]
Wang, X., Chang, P., and Gu, N., 2007, “Additive Perturbed Generalized Mandelbrot-Julia Sets,” Appl. Math. Comput., 189(1), pp. 754–765. [CrossRef]
Rani, M., and Agarwal, R., 2010, “Effect of Stochastic Noise on Superior Julia Sets,” J. Math. Imaging Vision, 36, pp. 63–68. [CrossRef]
Negi, A., and Rani, M., 2008, “A New Approach to Dynamic Noise on Superior Mandelbrot Set,” Chaos, Solitons, Fractals, 36(4), pp. 1089–1096. [CrossRef]
Wang, X., Jia, R., and Zhenfeng, Z., 2009, “The Generalized Mandelbrot Set Perturbed by Composing Noise of Additive and Multiplicative,” Appl. Math. Comput., 210(1), pp. 107–118. [CrossRef]
Wang, X., Jia, R., and Sun, Y., 2009, “The Generalized Julia Set Perturbed by Composing Additive and Multiplicative Noises,” Discrete Dyn. Nat. Soc., 2009 Article ID 781976, 18pages doi:10.1155/2009/781976.

Figures

Grahic Jump Location
Fig. 1

(a) SJ at s = 0.9 (b) SJ at low additive and low multiplicative noise (s, m, k) = (0.9, 0.01, 0.01)

Grahic Jump Location
Fig. 2

Effect of increasing strength of multiplicative noise on SJ at low additive noise m = 0.01 at s = 0.8 (row 1) and s = 0.9 (row 2)

Grahic Jump Location
Fig. 3

Effect of increasing additive noise for m ≤ 1 on SJ at low multiplicative noise k = 0.01 at s = 0.9 (row 1) and s = 0.8 (row 2)

Grahic Jump Location
Fig. 4

Effect of increasing additive noise for m > 1 on SJ at low multiplicative noise k = 0.01 at s = 0.9 (row 1) and s = 0.8 (row 2)

Grahic Jump Location
Fig. 5

Effect of higher additive noise and higher multiplicative noise at (m, k, s) = (0.9, 0.9, 0.9)

Grahic Jump Location
Fig. 6

Effect of higher additive noise and higher multiplicative noise at m > 1 and k > 1 at s = 0.9 (row 1) and s = 0.6 (row 2)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In