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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abdurrahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28
Adhikari SP, Yang C, Kim H, Chua LO (2012) Memristor bridge synapse-based neural network and its learning. IEEE Trans Neural Netw Learn Syst 23:1426–1435
Adhikari SP, Sad MP, Kim H, Chua LO (2013) Three fingerprints of memristor. IEEE Trans Circ Syst I Reg Papers 60(11):3008–3021
Albuquerque HA, Rubinger RM, Rech PC (2008) Self-similar structures in a 2D parameter-space of an inductorless Chua’s circuit. Phys Lett A 372:4793–4798
Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Commun Math Phys 79(4):573–576
Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, vol 581. Springer, Germany
Azar AT, Vaidyanathan S (2016) Advances in chaos theory and intelligent control. Springer, Berlin, Germany
Azar AT, Vaidyanathan S, Ouannas A (2017) Fractional order control and synchronization of chaotic systems. Springer, Berlin, Germany
Bao BC, Liu Z, Xu BP (2010) Dynamical analysis of memristor chaotic oscillator. Acta Phys Sin 59(6):3785–3793
Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240
Carroll TL, Pecora LM (1991) Synchronizing chaotic circuits. IEEE Trans Circ Syst 38(4):453–456
Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466
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):3298–3312
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):2825–2837
Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circ Theor 18(5):507–519
Chua LO (1994) Chua’s circuit: an overview ten years later. J Circ Syst Comput 04:117–159
Chua LO, Yang L (1988) Cellular neural networks: applications. IEEE Trans Circ Syst 35:1273–1290
Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circ Syst 35:1257–1272
Dudkowski D, Jafari S, Kapitaniaka T, Kuznetsov NV, Leonov GA, Prasad A (2016) Hidden attractors in dynamical systems. Phys Rep 637:1–50
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):1250,133
Fortuna L, Frasca M, Xibilia MG (2009) Chua’s circuit implementations: yesterday, today and tomorrow. World Scientific, Singapore
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):1955–1971
Itoh M, Chua LO (2008) Memristor oscillators. Int J Bifurc Chaos 18(11):3183–3206
Jiang GP, Zheng WX, Chen G (2004) Global chaos synchronization with channel time-delay. Chaos, Solitons & Fractals 20(2):267–275
Joglekar YN, Wolf SJ (2009) The elusive memristor: properties of basic electrical circuits. Eur J Phys 30(4):661–675
Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103
Khalil HK (2001) Nonlinear Syst, 3rd edn. Prentice Hall, New Jersey, USA
Kuznetsov NV, Leonov GA (2014) Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors. IFAC Proc Vol 47(3):5445–5454
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 477–503
Leonov GA, Kuznetsov NV, Vagaitsev VI (2011) Localization of hidden Chua’s attractors. Phys Lett A 375(23):2230–2233
Li D (2008) A three-scroll chaotic attractor. Phys Lett A 372(4):387–393
Li GH, Zhou SP, Yang K (2007) Controlling chaos in Colpitts oscillator. Chaos Solitons Fractals 33:582–587
Li H, Wang L, Duan S (2014) A memristor-mased scroll chaotic system—design, analysis and circuit implementation. Int J Bifurc Chaos 24(07):1450,099
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):1172–1188
Liu L, Wu X, Hu H (2004) Estimating system parameters of Chua’s circuit from synchronizing signal. Phys Lett A 324(1):36–41
Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141
Lü J, Chen G (2002) A new chaotic attractor coined. Int J Bifurc Chaos 12(3):659–661
Matsumoto T (1984) A chaotic attractor from Chua’s circuit. IEEE Trans Circ Syst 31:1055–1058
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 351–367
Muthuswamy B (2010) Implementing memristor based chaotic circuits. Int J Bifurc Chaos 20(5):1335–1350
Muthuswamy B, Chua LO (2010) Simplest chaotic circuit. Int J Bifurc Chaos 20(5):1567–1580
Muthuswamy B, Kokate P (2009) Memristor based chaotic circuits. IETE Tech Rev 26(6):417–429
Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824
Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096
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
Rasappan S, Vaidyanathan S (2012) Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East J Math Sci 67(2):265–287
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):343–365
Rasappan S, Vaidyanathan S (2012) Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback. Commun Comput Inf Sci 305:212–221
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):219–246
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
Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398
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
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):26–33
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
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):21–30
Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of three-scroll chaotic systems via adaptive control. Eur J Sci Res 72(4):504–522
Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156
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 59:1906–1918
Shin S, Kim K, Kang SM (2011) Memristor applications for programmable analog ICs. IEEE Trans Nanotechnol 410:266–274
Slotine J, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ, USA
Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50(2):647–650
Strukov D, Snider G, Stewart G, Williams R (2008) The missing memristor found. Nature 453:80–83
Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299
Sundarapandian V (2011) Output regulation of the Arneodo-Coullet chaotic system. Commun Comput Inf Sci 133:98–107
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
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):18–25
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
Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52
Sundarapandian V, Karthikeyan R (2012) Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control. J Eng Appl Sci 7(3):254–264
Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Model 55(7–8):1904–1915
Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing Chaotic systems. Int J Soft Comput 6(5):224–231
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):73–95
Tang F, Wang L (2005) An adaptive active control for the modified Chua’s circuit. Phys Lett A 346:342–346
Tetzlaff R (2014) Memristors and memristive systems. Springer, Berlin, Germany
Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos, Solitons Fractals 36:1315–1319
Utkin VI (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222
Utkin VI (1993) Sliding mode control design principles and applications to electric drives. IEEE Trans Ind Electr 40(1):23–36
Vaidyanathan S (2011) Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Adv Intell Syst Comput 176:329–337
Vaidyanathan S (2011) Hybrid chaos synchronization of Liu and Lü systems by active nonlinear control. Commun Comput Inf Sci 204:1–10
Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inf Sci 204:84–93
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
Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theor Appl 5(2):117–123
Vaidyanathan S (2012) Output regulation of the Liu chaotic system. Appl Mech Mater 110–116:3982–3989
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
Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143
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
Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10
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
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
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):41–53
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):207–217
Vaidyanathan S (2014) Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int J Model Identif Control 22(2):170–177
Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J PharmTech Res 8(4):632–640
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
Vaidyanathan S (2015) A novel chemical chaotic reactor system and its adaptive control. Int J ChemTech Res 8(7):146–158
Vaidyanathan S (2015) Adaptive backstepping control of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(2):256–261
Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J PharmTech Res 8(4):622–631
Vaidyanathan S (2015) Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(5):964–973
Vaidyanathan S (2015) Adaptive control of a chemical chaotic reactor. Int J PharmTech Res 8(3):377–382
Vaidyanathan S (2015) Adaptive control of the FitzHugh-Nagumo chaotic neuron model. Int J PharmTech Res 8(6):117–127
Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J ChemTech Res 8(2):612–621
Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J PharmTech Res 8(5):928–937
Vaidyanathan S (2015) Adaptive synchronization of novel 3-D chemical chaotic reactor systems. Int J ChemTech Res 8(7):159–171
Vaidyanathan S (2015) Adaptive synchronization of the identical FitzHugh-Nagumo chaotic neuron models. Int J PharmTech Res 8(6):167–177
Vaidyanathan S (2015) Analysis, control and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities. Kyungpook Math J 55:563–586
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):164–172
Vaidyanathan S (2015) Anti-synchronization of brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768
Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J PharmTech Res 8(5):956–963
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
Vaidyanathan S (2015) Coleman-Gomatam logarithmic competitive biology models and their ecological monitoring. Int J PharmTech Res 8(6):94–105
Vaidyanathan S (2015) Dynamics and control of brusselator chemical reaction. Int J ChemTech Res 8(6):740–749
Vaidyanathan S (2015) Dynamics and control of tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–803
Vaidyanathan S (2015) Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method. Int J ChemTech Res 8(7):209–221
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
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):206–217
Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J PharmTech Res 8(5):974–981
Vaidyanathan S (2015) Lotka-Volterra two species competitive biology models and their ecological monitoring. Int J PharmTech Res 8(6):32–44
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
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
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
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 19–38
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
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
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
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
Vaidyanathan S, Rajagopal K (2011) Anti-synchronization of Li and T chaotic systems by active nonlinear control. Commun Comput Inf Sci 198:175–184
Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of hyperchaotic Pang and Wang systems by active nonlinear control. Commun Comput Inf Sci 204:84–93
Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of Lü and Pan systems by adaptive nonlinear control. Commun Comput Inf Sci 205:193–202
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
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
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
Vaidyanathan S, Sampath S (2011) Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control. Commun Comput Inf Sci 205:156–164
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
Vaidyanathan S, Volos C (2016) Advances and applications in chaotic systems. Springer, Berlin, Germany
Vaidyanathan S, Volos C (2016) Advances and applications in nonlinear control systems. Springer, Berlin, Germany
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
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
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
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
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):5–28
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
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):232–244
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
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
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):135–158
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):74–82
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
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 9:861–867
Wang X, Ge C (2008) Controlling and tracking of Newton-Leipnik system via backstepping design. Int J Nonlinear Sci 5(2):133–139
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):5401–5405
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
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):2039–2047
Yang JJ, Strukov DB, Stewart DR (2013) Memristive devices for computing. Nat Nanotechnol 8:13–24
Zhou W, Xu Y, Lu H, Pan L (2008) On dynamics analysis of a new chaotic attractor. Phys Lett A 372(36):5773–5777
Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inf Manag 2:104–109
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Vaidyanathan, S. (2017). A Memristor-Based Hyperchaotic System with Hidden Attractor and Its Sliding Mode Control. 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_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-55598-0_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55597-3
Online ISBN: 978-3-319-55598-0
eBook Packages: EngineeringEngineering (R0)