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Erschienen in:
A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities

verfasst von : Sundarapandian Vaidyanathan, Ahmad Taher Azar

Erschienen in: Advances in Chaos Theory and Intelligent Control

Verlag: Springer International Publishing

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Abstract

In this work, we announce an eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities. The phase portraits of the eleven-term novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel hyperchaotic system has a unique equilibrium at the origin, which is a saddle point. The Lyapunov exponents of the novel hyperchaotic system are obtained as \(L_1 = 2.0836\), \(L_2 = 0.1707\), \(L_3 = 0\) and \(L_4 = -26.6499\). The maximal Lyapunov exponent of the novel hyperchaotic system is found as \(L_1 = 2.0836\). Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is derived as \(D_{KY} = 3.0846\). 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 system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.

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Vorheriges Kapitel Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities
Nächstes Kapitel A Novel 4-D Four-Wing Chaotic System with Four Quadratic Nonlinearities and Its Synchronization via Adaptive Control Method
Literatur
1.
Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141CrossRef
2.
Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398CrossRef
3.
Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Commun Math Phys 79(4):573–576MathSciNetMATHCrossRef
4.
5.
6.
7.
Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240
8.
Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos Solitons Fractals 36:1315–1319
9.
10.
Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inf Manage 2:104–109
11.
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):422–429MathSciNetMATH
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
14.
Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Model 55(7–8):1904–1915MathSciNetMATHCrossRef
15.
Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143MATH
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):53–65MathSciNet
17.
Vaidyanathan S (2014) A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J Math Sci 84(2):219–226MATH
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
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):41–53CrossRef
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):207–217MathSciNetCrossRef
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
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):164–172CrossRef
23.
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
24.
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
25.
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
26.
Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353MathSciNet
27.
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):375–403MathSciNetMATH
28.
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
29.
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
30.
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
31.
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
32.
Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096CrossRef
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
34.
Pham VT, Vaidyanathan S, Volos CK, Jafari S (2015) Hidden attractors in a chaotic system with an exponential nonlinear term. Eur Phys J 224(8):1507–1517
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):1424–1432MathSciNetCrossRef
36.
Li C, Liao X, Wong KW (2005) Lag synchronization of hyperchaos with application to secure communications. Chaos Solitons Fractals 23(1):183–193MathSciNetMATHCrossRef
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
38.
Hammami S (2015) State feedback-based secure image cryptosystem using hyperchaotic synchronization. ISA Trans 54:52–59CrossRef
39.
Rhouma R, Belghith S (2008) Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys Lett A 372(38):5973–5978MATHCrossRef
40.
Zhu C (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37CrossRef
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 105:62–78MathSciNetCrossRef
42.
Zhang H, Liao X, Yu J (2005) Fuzzy modeling and synchronization of hyperchaotic systems. Chaos Solitons Fractals 26(3):835–843MATHCrossRef
43.
Wei X, Yunfei F, Qiang L (2012) A novel four-wing hyper-chaotic system and its circuit implementation. Procedia Eng 29:1264–1269CrossRef
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):3518–3524CrossRef
45.
46.
Jia Q (2007) Hyperchaos generated from the Lorenz chaotic system and its control. Phys Lett A 366:217–222MATHCrossRef
47.
Chen A, Lu J, Lü J, Yu S (2006) Generating hyperchaotic Lü attractor via state feedback control. Phys A 364:103–110CrossRef
48.
Li X (2009) Modified projective synchronization of a new hyperchaotic system via nonlinear control. Commun Theoret Phys 52:274–278MathSciNetMATHCrossRef
49.
50.
Vaidyanathan S, VTP, Volos CK, (2015) A 5-D hyperchaotic Rikitake dynamo system with hidden attractors. Eur Phys J 224(8):1575–1592
51.
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):97–109MathSciNet
52.
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
53.
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):380–392CrossRef
54.
Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system. Stud Comput Intell 581:3–17CrossRef
55.
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):409–446MathSciNetMATH
56.
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):267–277CrossRef
57.
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):135–158MathSciNet
58.
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
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
60.
Azar AT (2010) Fuzzy systems. IN-TECH, Vienna, Austria
61.
Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, studies in computational intelligence, vol 581. Springer, Germany
62.
Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, studies in computational intelligence, vol 575. Springer, Germany
63.
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
64.
Azar AT, Zhu Q (2015) Advances and applications in sliding mode control systems, studies in computational intelligence, vol 576. Springer, GermanyMATH
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
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):2914–2923MathSciNetCrossRef
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):2254–2269MathSciNetCrossRef
68.
69.
Petrov V, Gaspar V, Masere J, Showalter K (1993) Controlling chaos in Belousov-Zhabotinsky reaction. Nature 361:240–243CrossRef
70.
Vaidyanathan S (2015) Adaptive control of a chemical chaotic reactor. Int J PharmTech Res 8(3):377–382
71.
Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J ChemTech Res 8(2):612–621
72.
Vaidyanathan S (2015) Anti-synchronization of Brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768
73.
Vaidyanathan S (2015) Dynamics and control of Brusselator chemical reaction. Int J ChemTech Res 8(6):740–749
74.
Vaidyanathan S (2015) Dynamics and control of Tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–803
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
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 30:189–198CrossRef
77.
Kyriazis M (1991) Applications of chaos theory to the molecular biology of aging. Exp Gerontol 26(6):569–572CrossRef
78.
Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J PharmTech Res 8(4):632–640
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
80.
Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J PharmTech Res 8(4):622–631
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
82.
Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J PharmTech Res 8(5):928–937
83.
Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J PharmTech Res 8(5):956–963
84.
Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J PharmTech Res 8(5):974–981
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
86.
Gibson WT, Wilson WG (2013) Individual-based chaos: extensions of the discrete logistic model. J Theoret Biol 339:84–92MathSciNetCrossRef
87.
Suérez I (1999) Mastering chaos in ecology. Ecol Model 117(2–3):305–314CrossRef
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 338:181–192CrossRef
89.
Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Sig Process Image Commun 29(8):902–913CrossRef
90.
Rhouma R, Belghith S (2011) Cryptoanalysis of a chaos based cryptosystem on DSP. Commun Nonlinear Sci Numer Simul 16(2):876–884MathSciNetMATHCrossRef
91.
Usama M, Khan MK, Alghatbar K, Lee C (2010) Chaos-based secure satellite imagery cryptosystem. Comput Math Appl 60(2):326–337MathSciNetMATHCrossRef
92.
Azar AT, Serrano FE (2014) Robust IMC-PID tuning for cascade control systems with gain and phase margin specifications. Neural Comput Appl 25(5):983–995CrossRef
93.
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
94.
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
95.
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
96.
Azar AT, Serrano FE (2015) 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
97.
Feki M (2003) An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18(1):141–148MathSciNetMATHCrossRef
98.
Murali K, Lakshmanan M (1998) Secure communication using a compound signal from generalized chaotic systems. Phys Lett A 241(6):303–310MATHCrossRef
99.
Zaher AA, Abu-Rezq A (2011) On the design of chaos-based secure communication systems. Commun Nonlinear Sci Numer Simul 16(9):3721–3727MathSciNetMATHCrossRef
100.
Mondal S, Mahanta C (2014) Adaptive second order terminal sliding mode controller for robotic manipulators. J Franklin Inst 351(4):2356–2377MathSciNetCrossRef
101.
Nehmzow U, Walker K (2005) Quantitative description of robot-environment interaction using chaos theory. Robot Auton Syst 53(3–4):177–193CrossRef
102.
Volos CK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61(12):1314–1322CrossRef
103.
Qu Z (2011) Chaos in the genesis and maintenance of cardiac arrhythmias. Prog Biophys Mol Biol 105(3):247–257CrossRef
104.
105.
106.
Li Z, Chen G (2006) Integration of fuzzy logic and chaos theory, studies in fuzziness and soft computing, vol 187. Springer, GermanyCrossRef
107.
Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94:13–21CrossRef
108.
Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256MATHCrossRef
109.
Lian S, Chen X (2011) Traceable content protection based on chaos and neural networks. Appl Soft Comput 11(7):4293–4301CrossRef
110.
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
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
112.
Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299MathSciNetMATH
113.
Vaidyanathan S (2011) Output regulation of Arneodo-Coullet chaotic system. Commun Comput Inf Sci 133:98–107CrossRef
114.
Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inf Sci 198:1–9CrossRef
115.
Sundarapandian V (2013) Adaptive control and synchronization design for the Lu-Xiao chaotic system. Lect Notes Electr Eng 131:319–327CrossRef
116.
Vaidyanathan S (2012) Adaptive controller and syncrhonizer design for the Qi-Chen chaotic system. Lect Notes Inst Comput Sci, Social-Inform Telecommun Eng 84:73–82
117.
Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10CrossRef
118.
Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theor Appl 5(2):117–123
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):15–20MathSciNet
120.
Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s jerk systems. Stud Comput Intell 581:39–58CrossRef
121.
Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103
122.
Sarasu P, Sundarapandian V (2011) Active controller design for generalized projective synchronization of four-scroll chaotic systems. Int J Syst Sig Control Eng Appl 4(2):26–33
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
124.
Vaidyanathan S, Rajagopal K (2011) Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic Lorenz systems by active non-linear control. Int J Syst Sig Control Eng Appl 4(3):55–61
125.
Vaidyanathan S, Rasappan S (2011) Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Commun Comput Inf Sci 198:10–17CrossRef
126.
Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156CrossRef
127.
Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Syst Sig Control Eng Appl 4(2):18–25
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
129.
Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52MATHCrossRef
130.
Vaidyanathan S (2012) Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Int J Control Theor Appl 5(1):41–59MathSciNet
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
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):28–37MATHCrossRef
133.
Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing chaotic systems. Int J Soft Comput 6(5):224–231CrossRef
134.
Vaidyanathan S (2014) Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int J Model, Ident Control 22(2):170–177CrossRef
135.
Vaidyanathan S, Sampath S (2012) Anti-synchronization of four-wing chaotic systems via sliding mode control. Int J Autom Comput 9(3):274–279CrossRef
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):92–100CrossRef
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):73–95MathSciNet
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
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):219–246MathSciNetMATH
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):3351–3364CrossRef
141.
Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice Hall, USA
Metadaten
Titel
Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities
verfasst von
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Copyright-Jahr
2016
Buch
Advances in Chaos Theory and Intelligent Control

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

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

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-30340-6_8