nach oben

Erschienen in:

2024 | OriginalPaper | Buchkapitel

Generalized Fractional-Order Complex Logistic Map and Fractals on FPGA

verfasst von : Sara M. Mohamed, Wafaa S. Sayed, Lobna A. Said, A. G. Radwan

Erschienen in: Advances in Nonlinear Dynamics, Volume III

Verlag: Springer Nature Switzerland

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper introduces a generalized fractional-order complex logistic map and the FPGA realization of a corresponding fractal generation application. The chaotic properties of the proposed map are studied through the bifurcation behavior and maximum Lyapunov exponent (MLE). A concise fractal generation process is presented, which results in designing and implementing an optimized hardware architecture. An efficient FPGA implementation of the fractal behavior is validated experimentally on Artix-7 FPGA board. An example of fractal implementation is verified, yielding a frequency of 24.34 MHz and a throughput of 0.292 Gbit/s. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Bird-Like Trajectories in 6D Chaotic System Integrated with Fractional Order Derivative, Memristor, and Encryption

Nächstes Kapitel Fractional Control Performance Assessment of the Nonlinear Mechanical Systems

Zidan, M.A., Radwan, A.G., Salama, K.N.: Random number generation based on digital differential chaos. In: 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 1–4. IEEE (2011)

Di Bernardo, M., Vasca, F.: Discrete-time maps for the analysis of bifurcations and chaos in dc/dc converters. IEEE Trans. Circuits Syst. I Fund. Theory Appl. 47(2), 130–143 (2000)CrossRef

Jiang, C.X., Carletta, J.E., Hartley, T.T., Veillette, R.J.: A systematic approach for implementing fractional-order operators and systems. IEEE J. Emerg. Sel. Top. Circuits Syst. 3(3), 301–312 (2013).CrossRef

Bouallegue, K., Chaari, A., Toumi, A.: Multi-scroll and multi-wing chaotic attractor generated with julia process fractal. Chaos Solitons Fractals 44(1-3), 79–85 (2011)MathSciNetCrossRef

AboAlNaga, B.M., Said, L.A., Madian, A.H., Radwan, A.G.: Analysis and fpga of semi-fractal shapes based on complex gaussian map. Chaos Solitons Fractals 142, 110493 (2021)MathSciNetCrossRef

Abo-Alnaga, B.-A. M., Said, L.A., Madian, A.H., Radwan, A.G.: Fpga realization of complex logistic map fractal behavior. Fractals 30(01), 2250023 (2022)CrossRef

Mohamed, S.M., Sayed, W.S., Said, L.A., Radwan, A.G.: Fpga realization of fractals based on a new generalized complex logistic map. Chaos Solitons Fractals 160, 112215 (2022)MathSciNetCrossRef

Wu, G.-C., Baleanu, D.: Discrete fractional logistic map and its chaos. Nonlinear Dyn. 75(1), 283–287 (2014)MathSciNetCrossRef

El Raheem, Z., Salman, S.: On a discretization process of fractional-order logistic differential equation. J. Egypt. Math. Soc. 22(3), 407–412 (2014)MathSciNetCrossRef

10.

Munkhammar, J.: Chaos in a fractional order logistic map. Fract. Calculus Appl. Anal. 16(3), 511–519 (2013)MathSciNetCrossRef

11.

Ismail, S.M., Said, L.A., Rezk, A.A., Radwan, A.G., Madian, A.H., Abu-Elyazeed, M.F., Soliman, A.M.: Generalized fractional logistic map encryption system based on fpga. AEU-Int. J. Electron. Commun. 80, 114–126 (2017)CrossRef

12.

Chen, L., Yin, H., Huang, T., Yuan, L., Zheng, S., Yin, L.: Chaos in fractional-order discrete neural networks with application to image encryption. Neural Networks 125, 174–184 (2020)CrossRef

13.

Khennaoui, A.-A., Ouannas, A., Bendoukha, S., Grassi, G., Lozi, R.P., Pham, V.-T.: On fractional-order discrete-time systems: Chaos, stabilization and synchronization. Chaos Solitons Fractals 119, 150–162 (2019)MathSciNetCrossRef

14.

Ben Slimane, N., Bouallegue, K., Machhout, M.: Designing a multi-scroll chaotic system by operating logistic map with fractal process. Nonlinear Dyn. 88(3), 1655–1675 (2017)CrossRef

15.

Rani, M., Agarwal, R.: Generation of fractals from complex logistic map. Chaos Solitons Fractals 42(1), 447–452 (2009)CrossRef

16.

Peitgen, H.-O., Jürgens, H., Saupe, D.: Fractals for the Classroom: Part One Introduction to Fractals and Chaos. Springer Science & Business Media, New York (2013)

17.

Banerjee, S., Hassan, M.K., Mukherjee, S., Gowrisankar, A.: Fractal Patterns in Nonlinear Dynamics and Applications. CRC Press, Boca Raton (2020)CrossRef

Titel: Generalized Fractional-Order Complex Logistic Map and Fractals on FPGA
verfasst von: Sara M. Mohamed
Wafaa S. Sayed
Lobna A. Said
A. G. Radwan
Verlag: Springer Nature Switzerland
Buch: Advances in Nonlinear Dynamics, Volume III
Print ISBN: 978-3-031-50634-5

Electronic ISBN: 978-3-031-50635-2

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-50635-2_35

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht