Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Mathematical Modelling of Chaotic Jerk Circuit and Its Application in Secure Communication System

Authors : Aceng Sambas, Mada Sanjaya WS, Mustafa Mamat, Rizki Putra Prastio

Published in: Advances in Chaos Theory and Intelligent Control

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In chaos-based secure communication schemes, a message signal is modulated to the chaotic signal at transmitter and at receiver the masking signals regenerated and subtracted from the receiver signal. In order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this chapter is to analyze the eigenvalue structures, various attractors, bifurcation diagram, Lyapunov exponent spectrum, FFT analysis, Poincare maps, while the analysis of the synchronization in the case of bidirectional coupling between two identical generated chaotic systems, has been presented. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling method scheme between two identical Jerk circuits in a secure communication system is presented in details.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Synchronization of Chaotic Dynamical Systems in Discrete-Time
next chapter Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities
Literature
1.
Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design. Studies in computational intelligence, vol 581. Springer, Berlin. ISBN 978-3-319-13131-3
2.
Azar A. T and Vaidyanathan S., 2015. Computational intelligence applications in modeling and control. Studies in computational intelligence, vol 575. Springer, Berlin. ISBN 978-3-319-11016-5
3.
Azar AT, Vaidyanathan S (2015) Handbook of research on advanced intelligent control engineering and automation. Advances in computational intelligence and robotics (ACIR) Book Series. IGI Global, USA
4.
Cao LY, Lai YC (1998) Antiphase synchronism in chaotic systems. Phys Rev E 58:382–386CrossRef
5.
Dong G, Zheng S, Tian L, Du R, Sun M, Shi Z (2009) The analysis of a novel 3-D autonomous system and circuit implementation. Phys Lett A 373:4227–4238MathSciNetCrossRefMATH
6.
Han F (2004) Multi-Scroll Chaos generation via linear systems and hysteresis function series. Dissertation. PhD thesis, Royal Melbourne Institute of Technology, Australia
7.
Li C, Wang J, Hu W (2012) Absolute term introduced to rebuild the chaotic attractor with constant Lyapunov exponent spectrum. Nonlinear Dyn. 68(4):575–587MathSciNetCrossRefMATH
8.
Li XF, Chlouverakis KE, Xu D-L (2009) Nonlinear dynamics and circuit realization of a new chaotic flow: a variant of Lorentz. Chen and L. Nonlinear Anal: Real World Appl 10:2357–2368
9.
Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130141
10.
Mainieri R, Rehacek J (1999) Projective synchronization in three dimensional Chaotic systems. Phys Rev Lett 82:3042 3045
11.
Nakajima K, Sawada Y (1979) Experimental studies on the weak coupling of oscillatory chemical reaction systems. J Chem Phys 72(4):2231–2234CrossRef
12.
Pandey A, Baghel RK, Singh RP (2012) Analysis and circuit realization of a new autonomous Chaotic System. Int J Electron Commun Eng 5:487–496
13.
Pandey A, Baghel RK, Singh RP (2013) An autonomous Chaotic circuit for wideband secure communication. Int J Eng Bus Enterp Appl 4(1):44–47
14.
15.
Peng JH, Ding EJ, Ding M, Yang W (1996) Synchronizing hyperchaos with a scalar transmitted signal. Phys Rev Lett 76:904CrossRef
16.
Pikovski AS (1984) On the interaction of strange attractors. Z Phys B: Condens Matter 55:149–154
17.
18.
Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI (1995) Generalized synchronization of Chaos in directionally coupled Chaotic systems. Phys Rev E 51:980–994CrossRef
19.
Sambas A, Sanjaya WS, Halimatussadiyah M (2012) Unidirectional Chaotic synchronization of Rossler circuit and its application for secure communication. WSEAS Trans Syst 11:506–515
20.
Sambas A, Sanjaya WSM, Mamat M, Halimatussadiyah M (2013) Design and analysis bidirectional Chaotic synchronization of Rossler circuit and its application for secure communication. Appl Math Sci 7(1):11–21
21.
Sambas A, Sanjaya WSM, Mamat M (2015) Bidirectional coupling scheme of Chaotic systems and its application in secure communication system. J Eng Sci Technol Rev 8(2):89–95
22.
Sanjaya WSM, Mamat M, Salleh Z, Mohd I (2011) Bidirectional Chaotic synchronization of Hindmarsh-Rose neuron model. Appl Math Sci 5(54):2685–2695MathSciNetMATH
23.
Sanjaya WSM, Mamat Mohd IM, Salleh Z (2012) Mathematical model of three species food chain interaction with mixed functional response. Int J Mod Phys: Conf Ser 9:334340
24.
Shinbrot T, Grebogi C, Wisdom J, Yorke JA (1992) Chaos in a double pendulum. Am J Phys 60:491–499CrossRef
25.
26.
Sprott JC (2000) Simple Chaotic systems and circuits. Am J Phys 68:758–763CrossRef
27.
Sprott JC (2010) Elegant Chaos algebraically simple chaotic flows. World Scientific, SingaporeCrossRefMATH
28.
Sprott JC (2004) Dynamical models of love. Nonlinear Dyn Psych Life Sci 8:303–314
29.
Vaidyanathan S, Azar AT (2015) Anti-synchronization of identical Chaotic systems using sliding mode control and an application to Vaidyanathan-Madhavan Chaotic systems. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems. Studies in computational intelligence book series, vol 576. Springer, Berlin, pp 527–547
30.
Vaidyanathan S, Azar AT (2015) Hybrid synchronization of identical Chaotic systems using sliding mode control and an application to Vaidyanathan Chaotic systems. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems. Studies in computational intelligence book series, vol 576. Springer, Berlin, pp 549–569
31.
Vaidyanathan S, Azar AT (2015) Analysis, control and synchronization of a nine-Term 3-D novel Chaotic system. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design. Studies in computational intelligence book series, vol 581. Springer, Berlin, pp 3–17
32.
Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design. Studies in computational intelligence, vol 581. Springer, Berlin, pp 19–38
33.
Vaidyanathan S, Azar AT, Rajagobal K, Alexander P (2015) Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronization via active control. Int J Modell Ident Control (IJMIC) (Forthcoming)
34.
Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global Chaos synchronization of Sprott’s Jerk systems. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design. Studies in computational intelligence, vol 581. Springer, Berlin, pp 19–58
35.
Vaidyanathan S, Karthikeyan R (2013) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Signal Syst Control Eng Appl 4:18–25
36.
Vaidyanathan S, Pakiriswamy S (2013) Generalized projective synchronization of six-term sundarapandian chaotic systems by adaptive control. Int J Control Theory Appl 6:153–163
37.
Vaidyanathan S, Sampath S, Azar AT (2015) Global chaos synchronization of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int J Modell Ident Control 23(1):92–100CrossRef
38.
Vaidyanathan S, Volos ChK, Pham VT, Madhavan K, Idowu BA (2014) adaptive backstepping control, synchronization and circuit simulation of a 3-D novel Jerk Chaotic system with two hyperbolic sinusoidal nonlinearities. Arch Control Sci 24(3):257–285MathSciNetMATH
39.
Vaidyanathan S, Volos ChK, Pham VT, Madhavan K (2015) Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation. Arch Control Sci 25(1):135–158MathSciNet
40.
Volos ChK, Kyprianidis IM, Stouboulos IN (2012) Synchronization phenomena in coupled nonlinear systems applied in economic cycles. WSEAS Trans Syst 11(12):681–690
41.
Volos ChK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61:1314–1322CrossRef
42.
Volos ChK, Kyprianidis IM, Stouboulos IN (2013) Text encryption scheme realized with a Chaotic Pseudo-random bit generator. J Eng Sci Technol Rev 6:914
43.
Volos ChK, Kyprianidis IM, Stavrinides SG, Stouboulos IN, Magafas I, Anagnostopoulos AN (2011) Nonlinear dynamics of a financial system from an engineers point of view. J Eng Sci Technol Rev 4:281–285
44.
Voss HU (2000) Anticipating Chaotic synchronization. Phys Rev E 61:5115–5119CrossRef
45.
Wang SX (1998) Simulation of Chaos synchronization, PhD thesis, University Western Ontario, London
46.
Wolf A (1986) Quantity Chaos with Lyapunov exponents. Princeton University Press, Chaos
47.
Zhang H (2010) Chaos synchronization and its application to secure communication. PhD thesis, University of Waterloo, Canada
48.
Zhu Q, Azar AT (2015) Complex system modelling and control through intelligent soft computations. Studies in fuzziness and soft computing, vol 319. Springer, Berlin. ISBN: 978-3-319-12882-5
Metadata
Title
Mathematical Modelling of Chaotic Jerk Circuit and Its Application in Secure Communication System
Authors
Aceng Sambas
Mada Sanjaya WS
Mustafa Mamat
Rizki Putra Prastio
Copyright Year
2016
Book
Advances in Chaos Theory and Intelligent Control

Print ISBN: 978-3-319-30338-3

Electronic ISBN: 978-3-319-30340-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-30340-6_6

Premium Partner

    Image Credits