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A Novel 4-D Hyperchaotic Thermal Convection System and Its Adaptive Control

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Advances in Chaos Theory and Intelligent Control

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 337))

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Abstract

In this work, we announce an eleven-term novel 4-D hyperchaotic thermal convection system with two quadratic nonlinearities. The phase portraits of the novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel 4-D hyperchaotic thermal convection system is obtained by introducing a feedback control to the 3-D thermal convection system obtained by Wang et al. (J Fluid Mech 237:479–498, 1992). The Lyapunov exponents of the novel hyperchaotic thermal convection system are obtained as \(L_1 = 0.40546\), \(L_2 = 0.03583\), \(L_3 = 0\) and \(L_4 = -6.44038\). Since there are two positive Lyapunov exponents for the novel 4-D thermal convection system, it is hyperchaotic. The Maximal Lyapunov Exponent (MLE) of the novel hyperchaotic system is found as \(L_1 = 0.40546\). Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is derived as \(D_{KY} = 3.0685\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic thermal convection system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical novel hyperchaotic thermal convection systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.

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References

  1. Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141

    Article  Google Scholar 

  2. Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398

    Article  Google Scholar 

  3. Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Common Math Phys 79(4):573–576

    Article  MathSciNet  MATH  Google Scholar 

  4. Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50(2):647–650

    Article  MathSciNet  Google Scholar 

  5. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurcat Chaos 9(7):1465–1466

    Article  MathSciNet  MATH  Google Scholar 

  6. Lü J, Chen G (2002) A new chaotic attractor coined. Int J Bifurcat Chaos 12(3):659–661

    Article  MathSciNet  MATH  Google Scholar 

  7. Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240

    Google Scholar 

  8. Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos Solitons Fractals 36:1315–1319

    Google Scholar 

  9. 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 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. 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):422–429

    Article  MathSciNet  MATH  Google Scholar 

  13. 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 

  14. 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 

  15. 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 

  16. 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 

  17. 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 

  18. Vaidyanathan S (2014) Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities. Eur Phys J 223(8):1519–1529

    Google Scholar 

  19. 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 

  20. 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 Ident Control 22(3):207–217

    Google Scholar 

  21. 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 

  22. 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 

  23. Vaidyanathan S, Rajagopal K, Volos CK, Kyprianidis IM, Stouboulos IN (2015c) 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 

  24. 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 

  25. 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):121–137

    Google Scholar 

  26. 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 

  27. 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 

  28. 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 

  29. 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 

  30. 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 

  31. 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 

  32. 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 

  33. 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 

  34. Pham VT, Vaidyanathan S, Volos CK, Jafari S (2015a) Hidden attractors in a chaotic system with an exponential nonlinear term. Eur Phys J 224(8):1507–1517

    Google Scholar 

  35. Filali RL, Benrejeb M, Borne P (2014) On observer-based secure communication design using discrete-time hyperchaotic systems. Commun Nonlinear Sci Numer Simul 19(5):1424–1432

    Article  MathSciNet  Google Scholar 

  36. Li C, Liao X, Wong KW (2005) Lag synchronization of hyperchaos with application to secure communications. Chaos Solitons Fractals 23(1):183–193

    Article  MathSciNet  MATH  Google Scholar 

  37. Wu X, Zhu C, Kan H (2015) An improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system. Appl Math Comput 252:201–214

    Google Scholar 

  38. Hammami S (2015) State feedback-based secure image cryptosystem using hyperchaotic synchronization. ISA Trans 54:52–59

    Article  Google Scholar 

  39. Rhouma R, Belghith S (2008) Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys Lett A 372(38):5973–5978

    Article  MATH  Google Scholar 

  40. Zhu C (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37

    Article  Google Scholar 

  41. Senouci A, Boukabou A (2014) Predictive control and synchronization of chaotic and hyperchaotic systems based on a \(T\)-\(S\) fuzzy model. Math Comput Simul 105:62–78

    Article  MathSciNet  Google Scholar 

  42. Zhang H, Liao X, Yu J (2005) Fuzzy modeling and synchronization of hyperchaotic systems. Chaos, Solitons Fractals 26(3):835–843

    Article  MATH  Google Scholar 

  43. Wei X, Yunfei F, Qiang L (2012) A novel four-wing hyper-chaotic system and its circuit implementation. Procedia Eng 29:1264–1269

    Article  Google Scholar 

  44. Yujun N, Xingyuan W, Mingjun W, Huaguang Z (2010) A new hyperchaotic system and its circuit implementation. Commun Nonlinear Sci Numer Simul 15(11):3518–3524

    Article  Google Scholar 

  45. Rössler OE (1979) An equation for hyperchaos. Phys Lett A 71:155–157

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  47. 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 

  48. Li X (2009) Modified projective synchronization of a new hyperchaotic system via nonlinear control. Commun Theoret Phys 52:274–278

    Article  MathSciNet  MATH  Google Scholar 

  49. Wang J, Chen Z (2008) A novel hyperchaotic system and its complex dynamics. Int J Bifurcat Chaos 18:3309–3324

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  52. Vaidyanathan S (2015) Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. Int J Model Ident Control 23(4):380–392

    Google Scholar 

  53. 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 

  54. Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system. Stud Comput Intell 581:3–17

    Google Scholar 

  55. 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 

  56. 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

    Google Scholar 

  57. 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):409–446

    Google Scholar 

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

    Google Scholar 

  59. 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 

  60. Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, studies in computational intelligence, vol 581. Springer, Germany

    Google Scholar 

  61. Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, studies in computational intelligence, vol 575. Springer, Germany

    Google Scholar 

  62. Azar AT, Vaidyanathan S (2015) Handbook of research on advanced intelligent control engineering and automation. Advances in computational intelligence and robotics (ACIR), IGI-Global, USA

    Google Scholar 

  63. Azar AT (2010) Fuzzy systems. IN-TECH, Vienna, Austria

    Google Scholar 

  64. Azar AT, Zhu Q (2015) Advances and applications in sliding mode control systems, studies in computational intelligence, vol 576. Springer, Germany

    MATH  Google Scholar 

  65. Zhu Q, Azar AT (2015) Complex system modelling and control through intelligent soft computations, studies in fuzzines and soft computing, vol 319. Springer, Germany

    Google Scholar 

  66. Kengne J, Chedjou JC, Kenne G, Kyamakya K (2012) Dynamical properties and chaos synchronization of improved Colpitts oscillators. Commun Nonlinear Sci Numer Simul 17(7):2914–2923

    Article  MathSciNet  Google Scholar 

  67. Sharma A, Patidar V, Purohit G, Sud KK (2012) Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping. Commun Nonlinear Sci Numer Simul 17(6):2254–2269

    Article  MathSciNet  Google Scholar 

  68. Gaspard P (1999) Microscopic chaos and chemical reactions. Phys A 263(1–4):315–328

    Article  MathSciNet  Google Scholar 

  69. Petrov V, Gaspar V, Masere J, Showalter K (1993) Controlling chaos in Belousov-Zhabotinsky reaction. Nature 361:240–243

    Article  Google Scholar 

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

    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) Anti-synchronization of Brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768

    Google Scholar 

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

    Google Scholar 

  74. Vaidyanathan S (2015) Dynamics and control of Tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–803

    Google Scholar 

  75. 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 

  76. Das S, Goswami D, Chatterjee S, Mukherjee S (2014) Stability and chaos analysis of a novel swarm dynamics with applications to multi-agent systems. Eng Appl Artif Intell 30:189–198

    Article  Google Scholar 

  77. Kyriazis M (1991) Applications of chaos theory to the molecular biology of aging. Exp Gerontol 26(6):569–572

    Article  Google Scholar 

  78. Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J PharmTech Res 8(4):632–640

    Google Scholar 

  79. Vaidyanathan S (2015) Adaptive backstepping control of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(2):256–261

    Google Scholar 

  80. Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J PharmTech Res 8(4):622–631

    Google Scholar 

  81. Vaidyanathan S (2015) Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(5):964–973

    Google Scholar 

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

    Google Scholar 

  83. Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J PharmTech Res 8(5):956–963

    Google Scholar 

  84. Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J PharmTech Res 8(5):974–981

    Google Scholar 

  85. Vaidyanathan S (2015) Synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method. Int J PharmTech Res 8(5):946–955

    Google Scholar 

  86. Gibson WT, Wilson WG (2013) Individual-based chaos: extensions of the discrete logistic model. J Theoret Biol 339:84–92

    Article  MathSciNet  Google Scholar 

  87. Suérez I (1999) Mastering chaos in ecology. Ecol Model 117(2–3):305–314

    Article  Google Scholar 

  88. Lang J (2015) Color image encryption based on color blend and chaos permutation in the reality-preserving multiple-parameter fractional Fourier transform domain. Opt Commun 338:181–192

    Article  Google Scholar 

  89. Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Sign Proces Image Commun 29(8):902–913

    Article  Google Scholar 

  90. Rhouma R, Belghith S (2011) Cryptoanalysis of a chaos based cryptosystem on DSP. Commun Nonlinear Sci Numer Simul 16(2):876–884

    Article  MathSciNet  MATH  Google Scholar 

  91. Usama M, Khan MK, Alghatbar K, Lee C (2010) Chaos-based secure satellite imagery cryptosystem. Comput Math Appl 60(2):326–337

    Article  MathSciNet  MATH  Google Scholar 

  92. Azar AT, Serrano FE (2015) Adaptive sliding mode control of the Furuta pendulum. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems, studies in computational intelligence, vol 576. Springer, Germany, pp 1–42

    Google Scholar 

  93. Azar AT, Serrano FE (2015) Deadbeat control for multivariable systems with time varying delays. In: Azar AT, Vaidyanathan S (eds) Chaos Modeling and control systems design, studies in computational intelligence, vol 581. Springer, Germany, pp 97–132

    Google Scholar 

  94. Azar AT, Serrano FE (2015) Design and modeling of anti wind up PID controllers. In: Zhu Q, Azar AT (eds) Complex system modelling and control through intelligent soft computations, studies in fuzziness and soft computing, vol 319. Springer, Germany, pp 1–44

    Google Scholar 

  95. Azar AT, Serrano FE (2014) Robust IMC-PID tuning for cascade control systems with gain and phase margin specifications. Neural Comput Appl 25(5):983–995

    Article  Google Scholar 

  96. Azar AT, Serrano FE (2015d) Stabilizatoin and control of mechanical systems with backlash. In: Azar AT, Vaidyanathan S (eds) Handbook of research on advanced intelligent control engineering and automation. Advances in computational intelligence and robotics (ACIR), IGI-Global, USA, pp 1–60

    Google Scholar 

  97. Feki M (2003) An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18(1):141–148

    Article  MathSciNet  MATH  Google Scholar 

  98. Murali K, Lakshmanan M (1998) Secure communication using a compound signal from generalized chaotic systems. Phys Lett A 241(6):303–310

    Article  MATH  Google Scholar 

  99. Zaher AA, Abu-Rezq A (2011) On the design of chaos-based secure communication systems. Commun Nonlinear Sci Numer Simul 16(9):3721–3727

    Article  MathSciNet  MATH  Google Scholar 

  100. Mondal S, Mahanta C (2014) Adaptive second order terminal sliding mode controller for robotic manipulators. J Franklin Inst 351(4):2356–2377

    Article  MathSciNet  Google Scholar 

  101. Nehmzow U, Walker K (2005) Quantitative description of robot-environment interaction using chaos theory. Robot Auton Sys 53(3–4):177–193

    Article  Google Scholar 

  102. Volos CK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61(12):1314–1322

    Article  Google Scholar 

  103. Qu Z (2011) Chaos in the genesis and maintenance of cardiac arrhythmias. Prog Biophys Mol Biol 105(3):247–257

    Article  Google Scholar 

  104. Witte CL, Witte MH (1991) Chaos and predicting varix hemorrhage. Med Hypotheses 36(4):312–317

    Article  MathSciNet  Google Scholar 

  105. Azar AT (2012) Overview of type-2 fuzzy logic systems. Int J Fuzzy Syst Appl 2(4):1–28

    Article  MathSciNet  Google Scholar 

  106. Li Z, Chen G (2006) Integration of fuzzy logic and chaos theory, studies in fuzziness and soft computing, vol 187. Springer, Germany

    Book  Google Scholar 

  107. Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94:13–21

    Article  Google Scholar 

  108. Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256

    Article  MATH  Google Scholar 

  109. Lian S, Chen X (2011) Traceable content protection based on chaos and neural networks. Appl Soft Comput 11(7):4293–4301

    Article  Google Scholar 

  110. Pham VT, Volos CK, Vaidyanathan S, Le TP, Vu VY (2015b) A memristor-based hyperchaotic system with hidden attractors: dynamics, synchronization and circuital emulating. J Eng Sci Technol Rev 8(2):205–214

    Google Scholar 

  111. 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 

  112. Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299

    MathSciNet  MATH  Google Scholar 

  113. Vaidyanathan S (2011) Output regulation of Arneodo-Coullet chaotic system. Commun Comput Inf Sci 133:98–107

    Google Scholar 

  114. Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inf Sci 198:1–9

    Google Scholar 

  115. Sundarapandian V (2013) Adaptive control and synchronization design for the Lu-Xiao chaotic system. Lect Notes Electr Eng 131:319–327

    Google Scholar 

  116. Vaidyanathan S (2012) Adaptive controller and syncrhonizer design for the Qi-Chen chaotic system. Lect Notes Inst Comput Sci Social-Informatics Telecommun Eng 84:73–82

    Google Scholar 

  117. Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  120. Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s jerk systems. Stud Comput Intell 581:39–58

    Google Scholar 

  121. Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103

    Google Scholar 

  122. Sarasu P, Sundarapandian V (2011) Active controller design for generalized projective synchronization of four-scroll chaotic systems. Int J Syst Sign Control Eng Appl 4(2):26–33

    Google Scholar 

  123. 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):216–223

    Google Scholar 

  124. Vaidyanathan S, Rajagopal K (2011) Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic Lorenz systems by active non-linear control. Int J Syst Sign Control Eng Appl 4(3):55–61

    Google Scholar 

  125. Vaidyanathan S, Rasappan S (2011) Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Commun Comput Inf Sci 198:10–17

    Article  Google Scholar 

  126. Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156

    Article  Google Scholar 

  127. Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Syst Sign Control Eng Appl 4(2):18–25

    Google Scholar 

  128. Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control. Eur J Sci Res 64(1):94–106

    Google Scholar 

  129. Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52

    Article  MATH  Google Scholar 

  130. Vaidyanathan S (2012) Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Int J Control Theor Appl 5(1):41–59

    Google Scholar 

  131. Vaidyanathan S, Pakiriswamy S (2013) Generalized projective synchronization of six-term Sundarapandian chaotic systems by adaptive control. Int J Control Theor Appl 6(2):153–163

    Google Scholar 

  132. Vaidyanathan S, Rajagopal K (2012) Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control. Int J Soft Comput 7(1):28–37

    Article  MATH  Google Scholar 

  133. 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 

  134. 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 

  135. Vaidyanathan S, Sampath S (2012) Anti-synchronization of four-wing chaotic systems via sliding mode control. Int J Autom Comput 9(3):274–279

    Article  Google Scholar 

  136. Vaidyanathan S, Sampath S, Azar AT (2015) Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int J Model Ident Control 23(1):92–100

    Google Scholar 

  137. Rasappan S, Vaidyanathan S (2013) Hybrid synchronization of \(n\)-scroll Chua circuits using adaptive backstepping control design with recursive feedback. Malays J Math Sci 73(1):73–95

    MathSciNet  Google Scholar 

  138. Rasappan S, Vaidyanathan S (2014) Global chaos synchronization of WINDMI and Coullet chaotic systems using adaptive backstepping control design. Kyungpook Math J 54(1):293–320

    Google Scholar 

  139. 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 7(2):219–246

    MathSciNet  MATH  Google Scholar 

  140. 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):3351–3364

    Article  Google Scholar 

  141. Wang Y, Singer J, Bau HH (1992) Controlling chaos in a thermal convection loop. J Fluid Mech 237:479–498

    Article  MathSciNet  Google Scholar 

  142. Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice Hall, New Jersey, USA

    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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  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S. (2016). A Novel 4-D Hyperchaotic Thermal Convection System and Its Adaptive Control. In: Azar, A., Vaidyanathan, S. (eds) Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-30340-6_4

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