Chaos in the APFM nonlinear adaptive filter

Color image encryption using chaotic nonlinear adaptive filter

“…The mathematical model of this APFM nonlinear adaptive filter is presented as [13] A ¼ −2μ 1 A sin 2 ϕ þ 2μ 1 sin ϕuðtÞ ω ¼ −μ 2 A 2 sin ð2ϕÞ þ 2μ 2 A cos ϕuðtÞ…”

Do chaos-based communication systems really transmit chaotic signals?

“…The encoding function (12) associated to the Hénon map has an interesting property: for a binary polar message, we can observe from (12) that s 2 ðnÞ ¼ x 2 1 ðnÞ. Thus, fðsðnÞÞ ¼ fðx 1 ðnÞÞ does not depend on m(n).…”

“…Again, we have assumed that the same encoding function of the previous example [Eq. (12)] with x 2 ðnÞ in place of x 1 ðnÞ as in [19] and a binary message. It is important to notice that, differently from the communication system based on the Hénon map, the matrices A t and A r are now time-dependent and contain the nonlinear encoding function.…”

“…This fact is particularly true when it comes to Signal Processing and Telecommunications, especially after the works by Pecora and Carroll [2] and Ott et al [3]. Chaos has appeared in different areas as digital and analog modulation, cryptography, pseudorandom sequences generation, watermarking, nonlinear adaptive filters, phase-locked loop networks, among others (see e.g., [4][5][6][7][8][9][10][11][12][13]). …”

Applying Estimation Techniques to Chaos-Based Digital Communications

“…Applications of chaos ranging from digital and analog modulation to cryptography, pseudorandom sequences generation and watermarking have been proposed (Kennedy & Kolumban, 2000;Kennedy, Setti & Rovatti, 2000;Stavroulakis, 2005;Tsekeridou et al, 2001). Chaos has also been shown in connection to devices used in signal processing such as nonlinear adaptive filters and phase-locked loop networks (Endo & Chua, 1988;Harb & Harb, 2004;Monteiro et al, 2009;Tavazoei & Haeri, 2009). In particular, many recent works have described digital modulations using chaotic carriers (Kennedy & Kolumban, 2000;Kennedy, Setti & Rovatti, 2000;Kolumban et al, 1997;Kolumban, Kennedy & Chua, 1998;Lau & Tse, 2003) even though their performance proved below that of equivalent conventional systems under additive white gaussian noise channel (Kaddoum et al, 2009;Williams, 2001).…”