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Adaptive Integral Sliding Mode Controller Design for the Regulation and Synchronization of a Novel Hyperchaotic Finance System with a Stable Equilibrium

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Applications of Sliding Mode Control in Science and Engineering

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

Abstract

Chaos and hyperchaos have important applications in finance, physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. 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. This work proposes a novel 4-D hyperchaotic finance system. We show that the hyperchaotic finance system has a unique equilibrium point, which is locally exponentially stable. Also, we show that the Lyapunov exponents of the hyperchaotic finance system are \(L_1 = 0.0365\), \(L_2 = 0.0172\), \(L_3 = 0\) and \(L_4 = -0.8727\). The Kaplan-Yorke dimension of the hyperchaotic finance system is derived as \(D_{KY} = 3.0615\), which shows the high complexity of the system. Next, an adaptive integral sliding mode control scheme is proposed for the global regulation of all the trajectories of the hyperchaotic finance system. Furthermore, an adaptive integral sliding mode control scheme is proposed for the global hyperchaos synchronization of identical hyperchaotic finance systems. The adaptive control mechanism helps the control design by estimating the unknown parameters. Numerical simulations using MATLAB are shown to illustrate all the main results derived in this work.

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References

  1. Akgul A, Hussain S, Pehlivan I (2016) A new three-dimensional chaotic system, its dynamical analysis and electronic circuit applications. Optik 127(18):7062–7071

    Google Scholar 

  2. Akgul A, Moroz I, Pehlivan I, Vaidyanathan S (2016) A new four-scroll chaotic attractor and its engineering applications. Optik 127(13):5491–5499

    Google Scholar 

  3. Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Azar AT, Vaidyanathan S (2016) Advances in chaos theory and intelligent control. Springer, Berlin

    Book  MATH  Google Scholar 

  5. Azar AT, Vaidyanathan S (2017) Fractional order control and synchronization of chaotic systems. Springer, Berlin

    Book  Google Scholar 

  6. Boulkroune A, Bouzeriba A, Bouden T (2016) Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems. Neurocomputing 173:606–614

    Article  MATH  Google Scholar 

  7. Burov DA, Evstigneev NM, Magnitskii NA (2017) On the chaotic dynamics in two coupled partial differential equations for evolution of surface plasmon polaritons. Commun Nonlinear Sci Numer Simul 46:26–36

    Article  MathSciNet  Google Scholar 

  8. Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213

    Article  Google Scholar 

  9. Chen A, Lu J, Lü J, Yu S (2006) Generating hyperchaotic Lü attractor via state feedback control. Phys A 364:103–110

    Article  Google Scholar 

  10. Chenaghlu MA, Jamali S, Khasmakhi NN (2016) A novel keyed parallel hashing scheme based on a new chaotic system. Chaos Solitons Fractals 87:216–225

    Article  MATH  Google Scholar 

  11. Dadras S, Momeni HR, Qi G, lin Wang Z, (2012) Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form. Nonlinear Dyn 67:1161–1173

    Google Scholar 

  12. Fallahi K, Leung H (2010) A chaos secure communication scheme based on multiplication modulation. Commun Nonlinear Sci Numer Simul 15(2):368–383

    Article  MATH  Google Scholar 

  13. Fontes RT, Eisencraft M (2016) A digital bandlimited chaos-based communication system. Commun Nonlinear Sci Numer Simul 37:374–385

    Article  MathSciNet  Google Scholar 

  14. Fotsa RT, Woafo P (2016) Chaos in a new bistable rotating electromechanical system. Chaos Solitons Fractals 93:48–57

    Article  MathSciNet  Google Scholar 

  15. Fujisaka H, Yamada T (1983) Stability theory of synchronized motion in coupled-oscillator systems. Progress Theoret Phys 63:32–47

    Article  MathSciNet  MATH  Google Scholar 

  16. Gao T, Chen Z, Yuan Z, Chen G (2006) A hyperchaos generated from Chen’s system. Int J Mod Phys C 17(4):471–478

    Article  MATH  Google Scholar 

  17. Huang D, Li H (1993) Theory and method of the nonlinear economics. Publishing House of Sichuan University, Chengdu

    Google Scholar 

  18. Jia Q (2007) Hyperchaos generated from the Lorenz chaotic system and its control. Phys Lett A 366(3):217–222

    Article  MATH  Google Scholar 

  19. Kacar S (2016) Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system. Optik 127(20):9551–9561

    Article  Google Scholar 

  20. Khalil HK (2002) Nonlinear systems. Prentice Hall, New York

    MATH  Google Scholar 

  21. 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, Germany, pp 477–503

    Chapter  Google Scholar 

  22. Li D (2008) A three-scroll chaotic attractor. Phys Lett A 372(4):387–393

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu H, Ren B, Zhao Q, Li N (2016) Characterizing the optical chaos in a special type of small networks of semiconductor lasers using permutation entropy. Opt Commun 359:79–84

    Google Scholar 

  24. Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36

    Google Scholar 

  25. Liu X, Mei W, Du H (2016) Simultaneous image compression, fusion and encryption algorithm based on compressive sensing and chaos. Opt Commun 366:22–32

    Google Scholar 

  26. 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, Germany, pp 351–367

    Chapter  Google Scholar 

  27. Pecora LM, Carroll TL (1991) Synchronizing chaotic circuits. IEEE Trans Circuits Syst 38:453–456

    Article  MATH  Google Scholar 

  28. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824

    Article  MathSciNet  MATH  Google Scholar 

  29. Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096

    Article  Google Scholar 

  30. Pham VT, Volos C, Jafari S, Wang X, Vaidyanathan S (2014) Hidden hyperchaotic attractor in a novel simple memristive neural network. Optoelectron Adv Mater Rapid Commun 8(11–12):1157–1163

    Google Scholar 

  31. Pham VT, Volos CK, Vaidyanathan S (2015) Multi-scroll chaotic oscillator based on a first-order delay differential equation. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design. Studies in computational intelligence, vol 581. Springer, Germany, pp 59–72

    Google Scholar 

  32. 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):205–214

    Google Scholar 

  33. Pham VT, Jafari S, Vaidyanathan S, Volos C, Wang X (2016) A novel memristive neural network with hidden attractors and its circuitry implementation. Sci China Technol Sci 59(3):358–363

    Google Scholar 

  34. Pham VT, Jafari S, Volos C, Giakoumis A, Vaidyanathan S, Kapitaniak T (2016) A chaotic system with equilibria located on the rounded square loop and its circuit implementation. IEEE Trans Circuits Syst II: Express Briefs 63(9):878–882

    Google Scholar 

  35. Pham VT, Jafari S, Volos C, Vaidyanathan S, Kapitaniak T (2016) A chaotic system with infinite equilibria located on a piecewise linear curve. Optik 127(20):9111–9117

    Google Scholar 

  36. Pham VT, Vaidyanathan S, Volos C, Jafari S, Kingni ST (2016) A no-equilibrium hyperchaotic system with a cubic nonlinear term. Optik 127(6):3259–3265

    Google Scholar 

  37. Pham VT, Vaidyanathan S, Volos CK, Hoang TM, Yem VV (2016) Dynamics, synchronization and SPICE implementation of a memristive system with hidden hyperchaotic attractor. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 35–52

    Google Scholar 

  38. Pham VT, Vaidyanathan S, Volos CK, Jafari S, Kuznetsov NV, Hoang TM (2016) A novel memristive time-delay chaotic system without equilibrium points. Eur Phys J Spec Top 225(1):127–136

    Google Scholar 

  39. Pham VT, Vaidyanathan S, Volos CK, Jafari S, Wang X (2016) A chaotic hyperjerk system based on memristive device. In: Vaidyanathan S, Volos C (eds) Advances and applications in chaotic systems. Springer, Berlin, pp 39–58

    Google Scholar 

  40. Rössler O (1979) An equation for hyperchaos. Phys Lett A 71(2–3):155–157

    Article  MathSciNet  MATH  Google Scholar 

  41. 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):1–6

    Google Scholar 

  42. Sampath S, Vaidyanathan S, Pham VT (2016) A novel 4-D hyperchaotic system with three quadratic nonlinearities, its adaptive control and circuit simulation. Int J Control Theory Appl 9(1):339–356

    Google Scholar 

  43. Shirkhani N, Khanesar M, Teshnehlab M (2016) Indirect model reference fuzzy control of SISO fractional order nonlinear chaotic systems. Procedia Comput Sci 102:309–316

    Article  Google Scholar 

  44. Slotine J, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  45. Sundarapandian V (2013) Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers. J Eng Sci Technol Rev 6(4):45–52

    Google Scholar 

  46. Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Model 55(7–8):1904–1915

    Article  MathSciNet  MATH  Google Scholar 

  47. Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing chaotic systems. Int J Soft Comput 6(5):224–231

    Article  Google Scholar 

  48. Szmit Z, Warminski J (2016) Nonlinear dynamics of electro-mechanical system composed of two pendulums and rotating hub. Procedia Eng 144:953–958

    Article  Google Scholar 

  49. Tacha OI, Volos CK, Kyprianidis IM, Stouboulos IN, Vaidyanathan S, Pham VT (2016) Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Appl Math Comput 276:200–217

    MathSciNet  MATH  Google Scholar 

  50. Utkin VI (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222

    Article  MathSciNet  MATH  Google Scholar 

  51. Utkin VI (1993) Sliding mode control design principles and applications to electric drives. IEEE Trans Industr Electron 40(1):23–36

    Article  Google Scholar 

  52. Vaidyanathan S (2011) Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Adv Intell Syst Comput 176:329–337

    Article  Google Scholar 

  53. Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theory Appl 5(2):117–123

    Google Scholar 

  54. Vaidyanathan S (2012) Sliding mode control based global chaos control of Liu-Liu-Liu-Su chaotic system. Int J Control Theory Appl 5(1):15–20

    Google Scholar 

  55. Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143

    Google Scholar 

  56. Vaidyanathan S (2013) A ten-term novel 4-D hyperchaotic system with three quadratic nonlinearities and its control. Int J Control Theory Appl 6(2):97–109

    Google Scholar 

  57. 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):53–65

    Google Scholar 

  58. Vaidyanathan S (2014) A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J Math Sci 84(2):219–226

    Google Scholar 

  59. 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):1519–1529

    Google Scholar 

  60. Vaidyanathan S (2014) Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int J Model Ident Control 22(1):41–53

    Google Scholar 

  61. Vaidyanathan S (2014) Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. Int J Model Ident Control 22(3):207–217

    Google Scholar 

  62. Vaidyanathan S (2014) Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int J Model Ident Control 22(2):170–177

    Google Scholar 

  63. Vaidyanathan S (2014) Qualitative analysis and control of an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. Int J Control Theory Appl 7(1):35–47

    Google Scholar 

  64. 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):106–115

    Google Scholar 

  65. Vaidyanathan S (2015) A novel chemical chaotic reactor system and its adaptive control. Int J ChemTech Res 8(7):146–158

    Google Scholar 

  66. Vaidyanathan S (2015) A novel chemical chaotic reactor system and its output regulation via integral sliding mode control. Int J ChemTech Res 8(11):669–683

    Google Scholar 

  67. Vaidyanathan S (2015) Active control design for the anti-synchronization of Lotka-Volterra biological systems with four competitive species. Int J PharmTech Res 8(7):58–70

    Google Scholar 

  68. Vaidyanathan S (2015) Adaptive control design for the anti-synchronization of novel 3-D chemical chaotic reactor systems. Int J ChemTech Res 8(11):654–668

    Google Scholar 

  69. Vaidyanathan S (2015) Adaptive control of a chemical chaotic reactor. Int J PharmTech Res 8(3):377–382

    Google Scholar 

  70. Vaidyanathan S (2015) Adaptive control of the FitzHugh-Nagumo chaotic neuron model. Int J PharmTech Res 8(6):117–127

    Google Scholar 

  71. Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J ChemTech Res 8(2):612–621

    Google Scholar 

  72. Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J PharmTech Res 8(5):928–937

    Google Scholar 

  73. Vaidyanathan S (2015) Adaptive synchronization of novel 3-D chemical chaotic reactor systems. Int J ChemTech Res 8(7):159–171

    Google Scholar 

  74. Vaidyanathan S (2015) Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. Int J Model Ident Control 23(2):164–172

    Google Scholar 

  75. Vaidyanathan S (2015) Anti-synchronization of brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768

    Google Scholar 

  76. Vaidyanathan S (2015) Anti-synchronization of brusselator chemical reaction systems via integral sliding mode control. Int J ChemTech Res 8(11):700–713

    Google Scholar 

  77. Vaidyanathan S (2015) Anti-synchronization of chemical chaotic reactors via adaptive control method. Int J ChemTech Res 8(8):73–85

    Google Scholar 

  78. Vaidyanathan S (2015) Anti-synchronization of the FitzHugh-Nagumo chaotic neuron models via adaptive control method. Int J PharmTech Res 8(7):71–83

    Google Scholar 

  79. Vaidyanathan S (2015) Chaos in neurons and synchronization of Birkhoff-Shaw strange chaotic attractors via adaptive control. Int J PharmTech Res 8(6):1–11

    Google Scholar 

  80. Vaidyanathan S (2015) Dynamics and control of brusselator chemical reaction. Int J ChemTech Res 8(6):740–749

    Google Scholar 

  81. Vaidyanathan S (2015) Dynamics and control of Tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–802

    Google Scholar 

  82. Vaidyanathan S (2015) Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method. Int J ChemTech Res 8(7):209–221

    Google Scholar 

  83. Vaidyanathan S (2015) Global chaos synchronization of Duffing double-well chaotic oscillators via integral sliding mode control. Int J ChemTech Res 8(11):141–151

    Google Scholar 

  84. Vaidyanathan S (2015) Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control method. Int J PharmTech Res 8(6):156–166

    Google Scholar 

  85. Vaidyanathan S (2015) Hybrid chaos synchronization of the FitzHugh-Nagumo chaotic neuron models via adaptive control method. Int J PharmTech Res 8(8):48–60

    Google Scholar 

  86. Vaidyanathan S (2015) Integral sliding mode control design for the global chaos synchronization of identical novel chemical chaotic reactor systems. Int J ChemTech Res 8(11):684–699

    Google Scholar 

  87. Vaidyanathan S (2015) Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method. Int J PharmTech Res 8(6):106–116

    Google Scholar 

  88. Vaidyanathan S (2015) Sliding controller design for the global chaos synchronization of forced Van der Pol chaotic oscillators. Int J PharmTech Res 8(7):100–111

    Google Scholar 

  89. Vaidyanathan S (2015) Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control. Int J ChemTech Res 8(6):818–827

    Google Scholar 

  90. Vaidyanathan S (2016) A no-equilibrium novel 4-D highly hyperchaotic system with four quadratic nonlinearities and its adaptive control. In: Vaidyanathan S, Volos C (eds) Advances and applications in nonlinear control systems. Springer, Berlin, pp 235–258

    Google Scholar 

  91. Vaidyanathan S (2016) A novel 3-D conservative chaotic system with a sinusoidal nonlinearity and its adaptive control. Int J Control Theory Appl 9(1):115–132

    Google Scholar 

  92. Vaidyanathan S (2016) A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control. Arch Control Sci 26(1):19–47

    Google Scholar 

  93. Vaidyanathan S (2016) A novel 3-D jerk chaotic system with two quadratic nonlinearities and its adaptive backstepping control. Int J Control Theory Appl 9(1):199–219

    Google Scholar 

  94. Vaidyanathan S (2016) A novel 4-D hyperchaotic thermal convection system and its adaptive control. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 75–100

    Google Scholar 

  95. Vaidyanathan S (2016) A novel 5-D hyperchaotic system with a line of equilibrium points and its adaptive control. In: Vaidyanathan S, Volos C (eds) Advances and applications in chaotic systems. Springer, Berlin, pp 471–494

    Google Scholar 

  96. Vaidyanathan S (2016) A novel highly hyperchaotic system and its adaptive control. In: Vaidyanathan S, Volos C (eds) Advances and applications in chaotic systems. Springer, Berlin, pp 513–535

    Google Scholar 

  97. Vaidyanathan S (2016) A novel hyperchaotic hyperjerk system with two nonlinearities, its analysis, adaptive control and synchronization via backstepping control method. Int J Control Theory Appl 9(1):257–278

    Google Scholar 

  98. Vaidyanathan S (2016) An eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities, analysis, control and synchronization via adaptive control method. Int J Control Theory Appl 9(1):21–43

    Google Scholar 

  99. Vaidyanathan S (2016) Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control method. Arch Control Sci 26(3):311–338

    Google Scholar 

  100. Vaidyanathan S (2016) Analysis, control and synchronization of a novel 4-D highly hyperchaotic system with hidden attractors. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 529–552

    Google Scholar 

  101. Vaidyanathan S (2016) Anti-synchronization of 3-cells cellular neural network attractors via integral sliding mode control. Int J PharmTech Res 9(1):193–205

    Google Scholar 

  102. Vaidyanathan S (2016) Global chaos control of the FitzHugh-Nagumo chaotic neuron model via integral sliding mode control. Int J PharmTech Res 9(4):413–425

    Google Scholar 

  103. Vaidyanathan S (2016) Global chaos control of the generalized Lotka-Volterra three-species system via integral sliding mode control. Int J PharmTech Res 9(4):399–412

    Google Scholar 

  104. Vaidyanathan S (2016) Global chaos regulation of a symmetric nonlinear gyro system via integral sliding mode control. Int J ChemTech Res 9(5):462–469

    Google Scholar 

  105. Vaidyanathan S (2016) Hybrid synchronization of the generalized Lotka-Volterra three-species biological systems via adaptive control. Int J PharmTech Res 9(1):179–192

    Google Scholar 

  106. Vaidyanathan S (2016) Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities. Arch Control Sci 26(4):471–495

    Google Scholar 

  107. Vaidyanathan S (2016) Mathematical analysis, adaptive control and synchronization of a ten-term novel three-scroll chaotic system with four quadratic nonlinearities. Int J Control Theory Appl 9(1):1–20

    Google Scholar 

  108. Vaidyanathan S (2016) Qualitative analysis and properties of a novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive control. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 455–480

    Google Scholar 

  109. 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 3–17

    Google Scholar 

  110. 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 19–38

    Google Scholar 

  111. Vaidyanathan S, Azar AT (2016) A novel 4-D four-wing chaotic system with four quadratic nonlinearities and its synchronization via adaptive control method. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 203–224

    Google Scholar 

  112. Vaidyanathan S, Azar AT (2016) Qualitative study and adaptive control of a novel 4-D hyperchaotic system with three quadratic nonlinearities. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 179–202

    Google Scholar 

  113. Vaidyanathan S, Azar AT (2016) Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system. Int J Intell Eng Inform 4(2):135–150

    Google Scholar 

  114. Vaidyanathan S, Boulkroune A (2016) A novel 4-D hyperchaotic chemical reactor system and its adaptive control. In: Vaidyanathan S, Volos C (eds) Advances and applications in chaotic systems. Springer, Berlin, pp 447–469

    Google Scholar 

  115. Vaidyanathan S, Madhavan K (2013) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system. Int J Control Theory Appl 6(2):121–137

    Google Scholar 

  116. Vaidyanathan S, Pakiriswamy S (2016) A five-term 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control method. Int J Control Theory Appl 9(1):61–78

    Google Scholar 

  117. 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):52–60

    Google Scholar 

  118. Vaidyanathan S, Pakiriswamy S (2016) Adaptive control and synchronization design of a seven-term novel chaotic system with a quartic nonlinearity. Int J Control Theory Appl 9(1):237–256

    Google Scholar 

  119. Vaidyanathan S, Rajagopal K (2016) Adaptive control, synchronization and LabVIEW implementation of Rucklidge chaotic system for nonlinear double convection. Int J Control Theory Appl 9(1):175–197

    Google Scholar 

  120. Vaidyanathan S, Rajagopal K (2016) Analysis, control, synchronization and LabVIEW implementation of a seven-term novel chaotic system. Int J Control Theory Appl 9(1):151–174

    Google Scholar 

  121. Vaidyanathan S, Sampath S (2011) Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control. Commun Comput Inf Sci 205:156–164

    Google Scholar 

  122. Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353

    MathSciNet  Google Scholar 

  123. Vaidyanathan S, Volos C (2016) Advances and applications in chaotic systems. Springer, Berlin

    Google Scholar 

  124. Vaidyanathan S, Volos C (2016) Advances and applications in nonlinear control systems. Springer, Berlin

    Google Scholar 

  125. Vaidyanathan S, Volos C (2017) Advances in memristors, memristive devices and systems. Springer, Berlin

    Google Scholar 

  126. Vaidyanathan S, Volos C, Pham VT (2014) Hyperchaos, adpative control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Arch Control Sci 24(4):409–446

    Google Scholar 

  127. 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):375–403

    Google Scholar 

  128. Vaidyanathan S, Azar AT, Rajagopal K, Alexander P (2015) Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control. Int J Model Ident Control 23(3):267–277

    Google Scholar 

  129. Vaidyanathan S, Pham VT, Volos CK (2015) A 5-D hyperchaotic Rikitake dynamo system with hidden attractors. Eur Phys J Spec Top 224(8):1575–1592

    Google Scholar 

  130. 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):130–141

    Google Scholar 

  131. 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):135–158

    MathSciNet  Google Scholar 

  132. 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):24–36

    Google Scholar 

  133. 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):181–191

    Google Scholar 

  134. Vaidyanathan S, Volos CK, Pham VT (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):232–244

    Google Scholar 

  135. 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 571–590

    Google Scholar 

  136. Vaidyanathan S, Volos CK, Pham VT (2016) Hyperchaos, control, synchronization and circuit simulation of a novel 4-D hyperchaotic system with three quadratic nonlinearities. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 297–325

    Chapter  Google Scholar 

  137. 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):157–173

    Google Scholar 

  138. Volos CK, Pham VT, Vaidyanathan S, Kyprianidis IM, Stouboulos IN (2015) Synchronization phenomena in coupled Colpitts circuits. J Eng Sci Technol Rev 8(2):142–151

    Google Scholar 

  139. Volos CK, Pham VT, Vaidyanathan S, Kyprianidis IM, Stouboulos IN (2016) Synchronization phenomena in coupled hyperchaotic oscillators with hidden attractors using a nonlinear open loop controller. In: Vaidyanathan S, Volos C (eds) Advances and applications in chaotic systems. Springer, Berlin, pp 1–38

    Google Scholar 

  140. Volos CK, Pham VT, Vaidyanathan S, Kyprianidis IM, Stouboulos IN (2016) The case of bidirectionally coupled nonlinear circuits via a memristor. In: Vaidyanathan S, Volos C (eds) Advances and applications in nonlinear control systems. Springer, Berlin, pp 317–350

    Google Scholar 

  141. Volos CK, Prousalis D, Kyprianidis IM, Stouboulos I, Vaidyanathan S, Pham VT (2016) Synchronization and anti-synchronization of coupled Hindmarsh-Rose neuron models. Int J Control Theory Appl 9(1):101–114

    Google Scholar 

  142. Volos CK, Vaidyanathan S, Pham VT, Maaita JO, Giakoumis A, Kyprianidis IM, Stouboulos IN (2016) A novel design approach of a nonlinear resistor based on a memristor emulator. In: Azar AT, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Springer, Berlin, pp 3–34

    Google Scholar 

  143. Wang B, Zhong SM, Dong XC (2016) On the novel chaotic secure communication scheme design. Commun Nonlinear Sci Numer Simul 39:108–117

    Article  MathSciNet  Google Scholar 

  144. Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Phys D 16:285–317

    Article  MathSciNet  MATH  Google Scholar 

  145. Wu T, Sun W, Zhang X, Zhang S (2016) Concealment of time delay signature of chaotic output in a slave semiconductor laser with chaos laser injection. Opt Commun 381:174–179

    Article  Google Scholar 

  146. Xu G, Liu F, Xiu C, Sun L, Liu C (2016) Optimization of hysteretic chaotic neural network based on fuzzy sliding mode control. Neurocomputing 189:72–79

    Google Scholar 

  147. Xu H, Tong X, Meng X (2016) An efficient chaos pseudo-random number generator applied to video encryption. Optik 127(20):9305–9319

    Google Scholar 

  148. Zhou W, Xu Y, Lu H, Pan L (2008) On dynamics analysis of a new chaotic attractor. Phys Lett A 372(36):5773–5777

    Article  MathSciNet  MATH  Google Scholar 

  149. Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inf Manage 2:104–109

    Google Scholar 

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  1. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

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    Sundarapandian Vaidyanathan

  2. Maritime College and Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung, Taiwan

    Chang-Hua Lien

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Vaidyanathan, S. (2017). Adaptive Integral Sliding Mode Controller Design for the Regulation and Synchronization of a Novel Hyperchaotic Finance System with a Stable Equilibrium. In: Vaidyanathan, S., Lien, CH. (eds) Applications of Sliding Mode Control in Science and Engineering. Studies in Computational Intelligence, vol 709. Springer, Cham. https://doi.org/10.1007/978-3-319-55598-0_13

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