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.
Issue Section:
Technical Brief
Keywords:
superior Julia set,
general noise,
additive noise,
multiplicative noise,
internal perturbation,
external perturbation
Topics:
Noise (Sound)
References
1.
Rani
, M.
, and Kumar
, V.
, 2004
, “Superior Julia Set
,” J. Korea Soc. Math. Educ. Ser. D: Res. Math. Educ.
, 8
(4
), pp. 261
–277
.210.101.116.28/W_kiss6/10303819_pv.pdf2.
Rani
, M.
, and Kumar
, V.
, 2004
, “Superior Mandelbrot Set
,” J. Korea Soc. Math. Educ. Ser. D: Res. Math. Educ.
, 8
(4
), pp. 279
–291
.210.101.116.28/W_kiss6/10303820_pv.pdf3.
Kumar
, M.
, and Rani
, M.
, 2005
, “A New Approach to Superior Julia Sets
,” J. Nature Phys. Sci.
, 19
(2
), pp. 148
–155
, MR2744660.4.
Rani
, M.
, and Agarwal
, R.
, 2009
, “Generation of Fractals from Complex Logistic Map
,” Chaos, Solitons Fractals
, 42
(1
), pp. 447
–452
.10.1016/j.chaos.2009.01.0115.
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
.10.1016/S0960-0779(97)00120-36.
Argyris
, J.
, Andreadis
, I.
, and Karakasidis
, T. E.
, 2000
, “On Perturbation of the Mandelbrot Map
,” Chaos, Solitons Fractals
, 11
(7
), pp. 1131
–1136
.10.1016/S0960-0779(99)00017-X7.
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
.10.1016/S0960-0779(99)00101-08.
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
.10.1016/S0960-0779(00)00257-59.
Wang
, X.
, Chang
, P.
, and Gu
, N.
, 2007
, “Additive Perturbed Generalized Mandelbrot-Julia Sets
,” Appl. Math. Comput.
, 189
(1
), pp. 754
–765
.10.1016/j.amc.2006.11.13710.
Rani
, M.
, and Agarwal
, R.
, 2010
, “Effect of Stochastic Noise on Superior Julia Sets
,” J. Math. Imaging Vision
, 36
, pp. 63
–68
.10.1007/s10851-009-0171-011.
Negi
, A.
, and Rani
, M.
, 2008
, “A New Approach to Dynamic Noise on Superior Mandelbrot Set
,” Chaos, Solitons, Fractals
, 36
(4
), pp. 1089
–1096
.10.1016/j.chaos.2006.07.02612.
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
.10.1016/j.amc.2008.12.01713.
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
, 18
pages doi:10.1155/2009/781976
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