A Memristor-Based Hyperchaotic System with Hidden Attractor and Its Sliding Mode Control

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 709)

Abstract

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention in the control literature. In this work, we study a memristor-based hyperchaotic system with hidden attractors. First, we study the dynamic properties of the memristor-based hyperchaotic system such as equilibria, Lyapunov exponents, Kaplan-Yorke dimension, etc. We obtain the Lyapunov exponents of the memristor-based system as \(L_1 = 0.2205\), \(L_2 = 0.0305\), \(L_3 = 0\) and \(L_4 = -10.7862\). Since there are two positive Lyapunov exponents, the memristor-based system is hyperchaotic. Also, the Kaplan-Yorke fractional dimension of the memristor-based hyperchaotic system is obtained as \(D_{KY} = 3.0233\), which shows the high complexity of the system. We show that the memristor-based hyperchaotic system has no equilibrium point, which shows that the system has a hidden attractor. Control and synchronization of chaotic and hyperchaotic systems are important research problems in chaos theory. Sliding mode control is an important method used to solve various problems in control systems engineering. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as insensitivity to parameter uncertainties and disturbance. Next, using integral sliding mode control, we design adaptive control and synchronization schemes for the memristor-based hyperchaotic system. The main adaptive control and synchronization results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the main results of this work.

Keywords

Memristor Hidden attractor Chaos Hyperchaos Adaptive control Synchronization Sliding mode control 

References

  1. 1.
    Abdurrahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28CrossRefGoogle Scholar
  2. 2.
    Adhikari SP, Yang C, Kim H, Chua LO (2012) Memristor bridge synapse-based neural network and its learning. IEEE Trans Neural Netw Learn Syst 23:1426–1435CrossRefGoogle Scholar
  3. 3.
    Adhikari SP, Sad MP, Kim H, Chua LO (2013) Three fingerprints of memristor. IEEE Trans Circ Syst I Reg Papers 60(11):3008–3021CrossRefGoogle Scholar
  4. 4.
    Albuquerque HA, Rubinger RM, Rech PC (2008) Self-similar structures in a 2D parameter-space of an inductorless Chua’s circuit. Phys Lett A 372:4793–4798CrossRefMATHGoogle Scholar
  5. 5.
    Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Commun Math Phys 79(4):573–576MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, vol 581. Springer, GermanyMATHGoogle Scholar
  7. 7.
    Azar AT, Vaidyanathan S (2016) Advances in chaos theory and intelligent control. Springer, Berlin, GermanyCrossRefMATHGoogle Scholar
  8. 8.
    Azar AT, Vaidyanathan S, Ouannas A (2017) Fractional order control and synchronization of chaotic systems. Springer, Berlin, GermanyCrossRefGoogle Scholar
  9. 9.
    Bao BC, Liu Z, Xu BP (2010) Dynamical analysis of memristor chaotic oscillator. Acta Phys Sin 59(6):3785–3793Google Scholar
  10. 10.
    Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240Google Scholar
  11. 11.
    Carroll TL, Pecora LM (1991) Synchronizing chaotic circuits. IEEE Trans Circ Syst 38(4):453–456CrossRefMATHGoogle Scholar
  12. 12.
    Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Chen WH, Wei D, Lu X (2014) Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control. Commun Nonlinear Sci Numer Simul 19(9):3298–3312MathSciNetCrossRefGoogle Scholar
  14. 14.
    Cheng CJ, Cheng CB (2013) An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network. Commun Nonlinear Sci Numer Simul 18(10):2825–2837MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circ Theor 18(5):507–519CrossRefGoogle Scholar
  16. 16.
    Chua LO (1994) Chua’s circuit: an overview ten years later. J Circ Syst Comput 04:117–159CrossRefGoogle Scholar
  17. 17.
    Chua LO, Yang L (1988) Cellular neural networks: applications. IEEE Trans Circ Syst 35:1273–1290Google Scholar
  18. 18.
    Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circ Syst 35:1257–1272Google Scholar
  19. 19.
    Dudkowski D, Jafari S, Kapitaniaka T, Kuznetsov NV, Leonov GA, Prasad A (2016) Hidden attractors in dynamical systems. Phys Rep 637:1–50MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fitch AL, Yu DS, Iu HHC, Sreeram V (2012) Hyperchaos in a memristor-based modified canonical Chua’s circuit. Int J Bifurc Chaos 22(6):1250,133Google Scholar
  21. 21.
    Fortuna L, Frasca M, Xibilia MG (2009) Chua’s circuit implementations: yesterday, today and tomorrow. World Scientific, SingaporeCrossRefGoogle Scholar
  22. 22.
    Gan Q, Liang Y (2012) Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J Frankl Inst 349(6):1955–1971MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Itoh M, Chua LO (2008) Memristor oscillators. Int J Bifurc Chaos 18(11):3183–3206MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Jiang GP, Zheng WX, Chen G (2004) Global chaos synchronization with channel time-delay. Chaos, Solitons & Fractals 20(2):267–275MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Joglekar YN, Wolf SJ (2009) The elusive memristor: properties of basic electrical circuits. Eur J Phys 30(4):661–675CrossRefMATHGoogle Scholar
  26. 26.
    Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103Google Scholar
  27. 27.
    Khalil HK (2001) Nonlinear Syst, 3rd edn. Prentice Hall, New Jersey, USAGoogle Scholar
  28. 28.
    Kuznetsov NV, Leonov GA (2014) Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors. IFAC Proc Vol 47(3):5445–5454CrossRefGoogle Scholar
  29. 29.
    Lakhekar GV, Waghmare LM, Vaidyanathan S (2016) Diving autopilot design for underwater vehicles using an adaptive neuro-fuzzy sliding mode controller. In: Vaidyanathan S, Volos C (eds) Advances and applications in nonlinear control systems. Springer, Berlin, Germany, pp 477–503CrossRefGoogle Scholar
  30. 30.
    Leonov GA, Kuznetsov NV, Vagaitsev VI (2011) Localization of hidden Chua’s attractors. Phys Lett A 375(23):2230–2233MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Li D (2008) A three-scroll chaotic attractor. Phys Lett A 372(4):387–393MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Li GH, Zhou SP, Yang K (2007) Controlling chaos in Colpitts oscillator. Chaos Solitons Fractals 33:582–587CrossRefGoogle Scholar
  33. 33.
    Li H, Wang L, Duan S (2014) A memristor-mased scroll chaotic system—design, analysis and circuit implementation. Int J Bifurc Chaos 24(07):1450,099Google Scholar
  34. 34.
    Li Q, Hu S, Tang S, Zeng G (2013) Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation. Int J Circ Theor Appl 42(11):1172–1188CrossRefGoogle Scholar
  35. 35.
    Liu L, Wu X, Hu H (2004) Estimating system parameters of Chua’s circuit from synchronizing signal. Phys Lett A 324(1):36–41MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141CrossRefGoogle Scholar
  37. 37.
    Lü J, Chen G (2002) A new chaotic attractor coined. Int J Bifurc Chaos 12(3):659–661MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Matsumoto T (1984) A chaotic attractor from Chua’s circuit. IEEE Trans Circ Syst 31:1055–1058MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Moussaoui S, Boulkroune A, Vaidyanathan S (2016) Fuzzy adaptive sliding-mode control scheme for uncertain underactuated systems. In: Vaidyanathan S, Volos C (eds) Advances and applications in nonlinear control systems. Springer, Berlin, Berlin, pp 351–367CrossRefGoogle Scholar
  40. 40.
    Muthuswamy B (2010) Implementing memristor based chaotic circuits. Int J Bifurc Chaos 20(5):1335–1350CrossRefMATHGoogle Scholar
  41. 41.
    Muthuswamy B, Chua LO (2010) Simplest chaotic circuit. Int J Bifurc Chaos 20(5):1567–1580CrossRefGoogle Scholar
  42. 42.
    Muthuswamy B, Kokate P (2009) Memristor based chaotic circuits. IETE Tech Rev 26(6):417–429CrossRefGoogle Scholar
  43. 43.
    Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824MathSciNetCrossRefMATHGoogle Scholar
  44. 44.
    Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096CrossRefGoogle Scholar
  45. 45.
    Pham VT, Volos CK, Vaidyanathan S, Le TP, Vu VY (2015) A memristor-based hyperchaotic system with hidden attractors: dynamics, synchronization and circuital emulating. J Eng Sci Technol Rev 8(2):205–214Google Scholar
  46. 46.
    Rasappan S, Vaidyanathan S (2012) Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East J Math Sci 67(2):265–287Google Scholar
  47. 47.
    Rasappan S, Vaidyanathan S (2012) Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Arch Control Sci 22(3):343–365Google Scholar
  48. 48.
    Rasappan S, Vaidyanathan S (2012) Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback. Commun Comput Inf Sci 305:212–221Google Scholar
  49. 49.
    Rasappan S, Vaidyanathan S (2013) Hybrid synchronization of \(n\)-scroll chaotic Chua circuits using adaptive backstepping control design with recursive feedback. Malays J Math Sci 7(2):219–246MathSciNetGoogle Scholar
  50. 50.
    Rasappan S, Vaidyanathan S (2014) Global chaos synchronization of WINDMI and Coullet chaotic systems using adaptive backstepping control design. Kyungpook Math J 54(1):293–320MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398CrossRefGoogle Scholar
  52. 52.
    Sampath S, Vaidyanathan S, Volos CK, Pham VT (2015) An eight-term novel four-scroll chaotic system with cubic nonlinearity and its circuit simulation. J Eng Sci Technol Rev 8(2):1–6Google Scholar
  53. 53.
    Sarasu P, Sundarapandian V (2011) Active controller design for the generalized projective synchronization of four-scroll chaotic systems. Int J Syst Signal Control Eng Appl 4(2):26–33Google Scholar
  54. 54.
    Sarasu P, Sundarapandian V (2011) The generalized projective synchronization of hyperchaotic Lorenz and hyperchaotic Qi systems via active control. Int J Soft Comput 6(5):216–223Google Scholar
  55. 55.
    Sarasu P, Sundarapandian V (2012) Adaptive controller design for the generalized projective synchronization of 4-scroll systems. Int J Syst Signal Control Eng Appl 5(2):21–30Google Scholar
  56. 56.
    Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of three-scroll chaotic systems via adaptive control. Eur J Sci Res 72(4):504–522Google Scholar
  57. 57.
    Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156Google Scholar
  58. 58.
    Shang Y, Fei W, Yu H (2012) Analysis and modeling of internal state variables for dynamic effects of nonvolatile memory devices. IEEE Trans Circ Syst I Reg Pap 59:1906–1918MathSciNetCrossRefGoogle Scholar
  59. 59.
    Shin S, Kim K, Kang SM (2011) Memristor applications for programmable analog ICs. IEEE Trans Nanotechnol 410:266–274CrossRefGoogle Scholar
  60. 60.
    Slotine J, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ, USAMATHGoogle Scholar
  61. 61.
    Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50(2):647–650MathSciNetCrossRefGoogle Scholar
  62. 62.
    Strukov D, Snider G, Stewart G, Williams R (2008) The missing memristor found. Nature 453:80–83CrossRefGoogle Scholar
  63. 63.
    Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299MathSciNetMATHGoogle Scholar
  64. 64.
    Sundarapandian V (2011) Output regulation of the Arneodo-Coullet chaotic system. Commun Comput Inf Sci 133:98–107Google Scholar
  65. 65.
    Sundarapandian V (2013) Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers. J Eng Sci Technol Rev 6(4):45–52Google Scholar
  66. 66.
    Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Syst Signal Control Eng Appl 4(2):18–25Google Scholar
  67. 67.
    Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control. Eur J Sci Res 64(1):94–106Google Scholar
  68. 68.
    Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52Google Scholar
  69. 69.
    Sundarapandian V, Karthikeyan R (2012) Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control. J Eng Appl Sci 7(3):254–264Google Scholar
  70. 70.
    Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Model 55(7–8):1904–1915MathSciNetCrossRefMATHGoogle Scholar
  71. 71.
    Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing Chaotic systems. Int J Soft Comput 6(5):224–231CrossRefGoogle Scholar
  72. 72.
    Suresh R, Sundarapandian V (2013) Global chaos synchronization of a family of \(n\)-scroll hyperchaotic Chua circuits using backstepping control with recursive feedback. Far East J Math Sci 73(1):73–95MATHGoogle Scholar
  73. 73.
    Tang F, Wang L (2005) An adaptive active control for the modified Chua’s circuit. Phys Lett A 346:342–346CrossRefMATHGoogle Scholar
  74. 74.
    Tetzlaff R (2014) Memristors and memristive systems. Springer, Berlin, GermanyCrossRefGoogle Scholar
  75. 75.
    Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos, Solitons Fractals 36:1315–1319MathSciNetCrossRefMATHGoogle Scholar
  76. 76.
    Utkin VI (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222MathSciNetCrossRefMATHGoogle Scholar
  77. 77.
    Utkin VI (1993) Sliding mode control design principles and applications to electric drives. IEEE Trans Ind Electr 40(1):23–36CrossRefGoogle Scholar
  78. 78.
    Vaidyanathan S (2011) Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Adv Intell Syst Comput 176:329–337Google Scholar
  79. 79.
    Vaidyanathan S (2011) Hybrid chaos synchronization of Liu and Lü systems by active nonlinear control. Commun Comput Inf Sci 204:1–10Google Scholar
  80. 80.
    Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inf Sci 204:84–93Google Scholar
  81. 81.
    Vaidyanathan S (2012) Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Int J Control Theor Appl 5(1):41–59Google Scholar
  82. 82.
    Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theor Appl 5(2):117–123Google Scholar
  83. 83.
    Vaidyanathan S (2012) Output regulation of the Liu chaotic system. Appl Mech Mater 110–116:3982–3989Google Scholar
  84. 84.
    Vaidyanathan S (2012) Sliding mode control based global chaos control of Liu-Liu-Liu-Su chaotic system. Int J Control Theor Appl 5(1):15–20Google Scholar
  85. 85.
    Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143Google Scholar
  86. 86.
    Vaidyanathan S (2013) Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters. J Eng Sci Technol Rev 6(4):53–65Google Scholar
  87. 87.
    Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10Google Scholar
  88. 88.
    Vaidyanathan S (2014) A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J Math Sci 84(2):219–226Google Scholar
  89. 89.
    Vaidyanathan S (2014) Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities. Eur Phys J Spec Top 223(8):1519–1529Google Scholar
  90. 90.
    Vaidyanathan S (2014) Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int J Model Identif Control 22(1):41–53Google Scholar
  91. 91.
    Vaidyanathan S (2014) Generalized projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. Int J Model Identif Control 22(3):207–217Google Scholar
  92. 92.
    Vaidyanathan S (2014) Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int J Model Identif Control 22(2):170–177Google Scholar
  93. 93.
    Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J PharmTech Res 8(4):632–640Google Scholar
  94. 94.
    Vaidyanathan S (2015) A 3-D novel highly chaotic system with four quadratic nonlinearities, its adaptive control and anti-synchronization with unknown parameters. J Eng Sci Technol Rev 8(2):106–115Google Scholar
  95. 95.
    Vaidyanathan S (2015) A novel chemical chaotic reactor system and its adaptive control. Int J ChemTech Res 8(7):146–158Google Scholar
  96. 96.
    Vaidyanathan S (2015) Adaptive backstepping control of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(2):256–261Google Scholar
  97. 97.
    Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J PharmTech Res 8(4):622–631Google Scholar
  98. 98.
    Vaidyanathan S (2015) Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(5):964–973Google Scholar
  99. 99.
    Vaidyanathan S (2015) Adaptive control of a chemical chaotic reactor. Int J PharmTech Res 8(3):377–382Google Scholar
  100. 100.
    Vaidyanathan S (2015) Adaptive control of the FitzHugh-Nagumo chaotic neuron model. Int J PharmTech Res 8(6):117–127Google Scholar
  101. 101.
    Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J ChemTech Res 8(2):612–621Google Scholar
  102. 102.
    Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J PharmTech Res 8(5):928–937Google Scholar
  103. 103.
    Vaidyanathan S (2015) Adaptive synchronization of novel 3-D chemical chaotic reactor systems. Int J ChemTech Res 8(7):159–171Google Scholar
  104. 104.
    Vaidyanathan S (2015) Adaptive synchronization of the identical FitzHugh-Nagumo chaotic neuron models. Int J PharmTech Res 8(6):167–177Google Scholar
  105. 105.
    Vaidyanathan S (2015) Analysis, control and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities. Kyungpook Math J 55:563–586Google Scholar
  106. 106.
    Vaidyanathan S (2015) Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. Int J Model Identif Control 23(2):164–172Google Scholar
  107. 107.
    Vaidyanathan S (2015) Anti-synchronization of brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768Google Scholar
  108. 108.
    Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J PharmTech Res 8(5):956–963Google Scholar
  109. 109.
    Vaidyanathan S (2015) Chaos in neurons and synchronization of Birkhoff-Shaw strange chaotic attractors via adaptive control. Int J PharmTech Res 8(6):1–11Google Scholar
  110. 110.
    Vaidyanathan S (2015) Coleman-Gomatam logarithmic competitive biology models and their ecological monitoring. Int J PharmTech Res 8(6):94–105Google Scholar
  111. 111.
    Vaidyanathan S (2015) Dynamics and control of brusselator chemical reaction. Int J ChemTech Res 8(6):740–749Google Scholar
  112. 112.
    Vaidyanathan S (2015) Dynamics and control of tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–803Google Scholar
  113. 113.
    Vaidyanathan S (2015) Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method. Int J ChemTech Res 8(7):209–221Google Scholar
  114. 114.
    Vaidyanathan S (2015) Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control method. Int J PharmTech Res 8(6):156–166Google Scholar
  115. 115.
    Vaidyanathan S (2015) Global chaos synchronization of the Lotka-Volterra biological systems with four competitive species via active control. Int J PharmTech Res 8(6):206–217Google Scholar
  116. 116.
    Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J PharmTech Res 8(5):974–981Google Scholar
  117. 117.
    Vaidyanathan S (2015) Lotka-Volterra two species competitive biology models and their ecological monitoring. Int J PharmTech Res 8(6):32–44Google Scholar
  118. 118.
    Vaidyanathan S (2015) Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method. Int J PharmTech Res 8(6):106–116Google Scholar
  119. 119.
    Vaidyanathan S (2016) Anti-synchronization of 3-cells Cellular Neural Network attractors via integral sliding mode control. Int J PharmTech Res 9(1):193–205Google Scholar
  120. 120.
    Vaidyanathan S (2016) Global chaos regulation of a symmetric nonlinear gyro system via integral sliding mode control. Int J ChemTech Res 9(5):462–469Google Scholar
  121. 121.
    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, Germany, pp 19–38Google Scholar
  122. 122.
    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 modelling and control systems design. Studies in computational intelligence, vol 581. Springer, Germany, pp 19–38Google Scholar
  123. 123.
    Vaidyanathan S, Madhavan K (2013) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system. Int J Control Theor Appl 6(2):121–137Google Scholar
  124. 124.
    Vaidyanathan S, Pakiriswamy S (2013) Generalized projective synchronization of six-term Sundarapandian chaotic systems by adaptive control. Int J Control Theor Appl 6(2):153–163Google Scholar
  125. 125.
    Vaidyanathan S, Pakiriswamy S (2015) A 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control. J Eng Sci Technol Rev 8(2):52–60Google Scholar
  126. 126.
    Vaidyanathan S, Rajagopal K (2011) Anti-synchronization of Li and T chaotic systems by active nonlinear control. Commun Comput Inf Sci 198:175–184Google Scholar
  127. 127.
    Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of hyperchaotic Pang and Wang systems by active nonlinear control. Commun Comput Inf Sci 204:84–93Google Scholar
  128. 128.
    Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of Lü and Pan systems by adaptive nonlinear control. Commun Comput Inf Sci 205:193–202Google Scholar
  129. 129.
    Vaidyanathan S, Rajagopal K (2012) Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control. Int J Soft Comput 7(1):28–37CrossRefMATHGoogle Scholar
  130. 130.
    Vaidyanathan S, Rasappan S (2011) Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Commun Comput Inf Sci 198:10–17Google Scholar
  131. 131.
    Vaidyanathan S, Rasappan S (2014) Global chaos synchronization of \(n\)-scroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arab J Sci Eng 39(4):3351–3364CrossRefGoogle Scholar
  132. 132.
    Vaidyanathan S, Sampath S (2011) Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control. Commun Comput Inf Sci 205:156–164Google Scholar
  133. 133.
    Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353MathSciNetGoogle Scholar
  134. 134.
    Vaidyanathan S, Volos C (2016) Advances and applications in chaotic systems. Springer, Berlin, GermanyGoogle Scholar
  135. 135.
    Vaidyanathan S, Volos C (2016) Advances and applications in nonlinear control systems. Springer, Berlin, GermanyGoogle Scholar
  136. 136.
    Vaidyanathan S, Volos C, Pham VT (2014) Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Arch Control Sci 24(4):409–446Google Scholar
  137. 137.
    Vaidyanathan S, Volos C, 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):375–403Google Scholar
  138. 138.
    Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s jerk systems. Stud Comput Intell 581:39–58Google Scholar
  139. 139.
    Vaidyanathan S, Rajagopal K, Volos CK, Kyprianidis IM, Stouboulos IN (2015) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J Eng Sci Technol Rev 8(2):130–141Google Scholar
  140. 140.
    Vaidyanathan S, Volos C, 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):5–28Google Scholar
  141. 141.
    Vaidyanathan S, Volos CK, Kyprianidis IM, Stouboulos IN, Pham VT (2015) Analysis, adaptive control and anti-synchronization of a six-term novel jerk chaotic system with two exponential nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):24–36Google Scholar
  142. 142.
    Vaidyanathan S, Volos CK, Madhavan K (2015) Analysis, control, synchronization and SPICE implementation of a novel 4-D hyperchaotic Rikitake dynamo System without equilibrium. J Eng Sci Technol Rev 8(2):232–244Google Scholar
  143. 143.
    Vaidyanathan S, Volos CK, Pham VT (2015) Analysis, adaptive control and adaptive synchronization of a nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):181–191Google Scholar
  144. 144.
    Vaidyanathan S, Volos CK, Pham VT (2015) Global chaos control of a novel nine-term chaotic system via sliding mode control. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems. Studies in computational intelligence, vol 576. Springer, Germany, pp 571–590Google Scholar
  145. 145.
    Vaidyanathan S, Volos CK, 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):135–158Google Scholar
  146. 146.
    Vaidyanathan S, Volos CK, Rajagopal K, Kyprianidis IM, Stouboulos IN (2015) Adaptive backstepping controller design for the anti-synchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementation. J Eng Sci Technol Rev 8(2):74–82Google Scholar
  147. 147.
    Volos CK, Kyprianidis IM, Stouboulos IN, Tlelo-Cuautle E, Vaidyanathan S (2015) Memristor: a new concept in synchronization of coupled neuromorphic circuits. J Eng Sci Technol Rev 8(2):157–173Google Scholar
  148. 148.
    Wang L, Zhang C, Chen L, Lai J, Tong J (2012) A novel memristor-based rSRAM structure for multiple-bit upsets immunity. IEICE Electron Express 9:861–867Google Scholar
  149. 149.
    Wang X, Ge C (2008) Controlling and tracking of Newton-Leipnik system via backstepping design. Int J Nonlinear Sci 5(2):133–139MathSciNetMATHGoogle Scholar
  150. 150.
    Wang X, Xu B, Luo C (2012) An asynchronous communication system based on the hyperchaotic system of 6th-order cellular neural network. Opt Commun 285(24):5401–5405Google Scholar
  151. 151.
    Wei Z, Yang Q (2010) Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci. Appl Math Comput 217(1):422–429MathSciNetMATHGoogle Scholar
  152. 152.
    Xiao X, Zhou L, Zhang Z (2014) Synchronization of chaotic Lur’e systems with quantized sampled-data controller. Commun Nonlinear Sci Numer Simul 19(6):2039–2047MathSciNetCrossRefGoogle Scholar
  153. 153.
    Yang JJ, Strukov DB, Stewart DR (2013) Memristive devices for computing. Nat Nanotechnol 8:13–24CrossRefGoogle Scholar
  154. 154.
    Zhou W, Xu Y, Lu H, Pan L (2008) On dynamics analysis of a new chaotic attractor. Phys Lett A 372(36):5773–5777MathSciNetCrossRefMATHGoogle Scholar
  155. 155.
    Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inf Manag 2:104–109Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Research and Development CentreVel Tech UniversityAvadi, ChennaiIndia

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