Title

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Journal title

Archives of Control Sciences

Yearbook

2016

Issue

No 3

Authors

Sundarapandian Vaidyanathan

Divisions of PAS

Nauki Techniczne

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

DOI: 10.1515/acsc-2016-0018 ; ISSN 1230-2384

Source

Archives of Control Sciences; 2016; No 3

References

RÖSSLER (1979), An equation for hyperchaos, Physics Letters A, 52, 155, doi.org/10.1016/0375-9601(79)90150-6 ; LI (2005), Lag synchronization of hyperchaos with application to secure communications Solitons and, Chaos Fractals, 44, 183, doi.org/10.1016/j.chaos.2004.04.025 ; VAIDYANATHAN (2014), Hyperchaos adaptive control and synchronization of a novel hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation of Control, Archives Sciences, 63, 409. ; VAIDYANATHAN (2016), A novel jerk chaotic system with three quadratic nonlinearities and its adaptive control of Control, Archives Sciences, 27, 19. ; SUNDARAPANDIAN (2011), Anti - synchronization of Lü and Pan chaotic systems by adaptive nonlinear control of Scientific Research, European Journal, 78, 94. ; YASSEN (2007), Controlling synchronization and tracking chaotic Liu system using active backstepping design, Physics Letters A, 73, 582, doi.org/10.1016/j.physleta.2006.08.067 ; VAIDYANATHAN (2015), hyperchaotic Rikitake dynamo system with hidden attractors :, European Physical Journal Special Topics, 66, 1575, doi.org/10.1140/epjst/e2015-02481-0 ; LORENZ (1963), Deterministic nonperiodic flow of the Atmospheric, Journal Sciences, 3, 130. ; VAIDYANATHAN (2016), Mathematical analysis adaptive control and synchronization of a ten - term novel three - scroll chaotic system with four quadratic nonlinearities of Control Theory and Applications, International Journal, 30, 1. ; VAIDYANATHAN (2014), Analysis and adaptive synchronization of eight - term polynomial chaotic systems with three quadratic nonlinearities :, European Physical Journal Special Topics, 20, 1519, doi.org/10.1140/epjst/e2014-02114-2 ; PHAM (2016), A novel memristive time - delay chaotic system without equilibrium points :, European Physical Journal Special Topics, 40, 127, doi.org/10.1140/epjst/e2016-02625-8 ; VAIDYANATHAN (2014), Adaptive backstepping control synchronization and circuit simulation of a novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities of Control, Archives Sciences, 21, 257. ; VAIDYANATHAN (2015), Analysis control synchronization and SPICE implementation of a novel hyperchaotic Rikitake dynamo system without equilibrium of and Technology, Journal Engineering Science Review, 65, 232. ; JIA (2007), Hyperchaos generated from the Lorenz chaotic system and its control, Physics Letters A, 58, 217. ; SUNDARAPANDIAN (2013), Analysis and anti - synchronization of a novel chaotic system via active and adaptive controllers of and Technology, Journal Engineering Science Review, 14, 45. ; SUNDARAPANDIAN (2012), Analysis control synchronization and circuit design of a novel chaotic system and Computer Modelling, Mathematical, 13, 1904. ; LIU (2013), Color image encryption using Choquet fuzzy integral and hyper chaotic system, Optik, 49, 3257. ; PHAM (2014), Constructing a novel no - equilibrium chaotic system of Bifurcation and, International Journal Chaos, 37, 1450073, doi.org/10.1142/S0218127414500734 ; SPROTT (2010), Elegant Chaos World Scientific, Singapore, 43. ; VAIDYANATHAN (2015), Analysis adaptive control and synchronization of a novel hyperchaotic hyperjerk system and its SPICE implementation of Control, Archives Sciences, 64, 135. ; CHLOUVERAKIS (2006), Chaotic hyperjerk systems Solitons and, Chaos Fractals, 71, 739, doi.org/10.1016/j.chaos.2005.08.019 ; VAIDYANATHAN (2016), A novel jerk chaotic system with two quadratic nonlinearities and its adaptive control of Control Theory and Applications, International Journal, 34, 199. ; LI (2009), Modified projective synchronization of a new hyperchaotic system via nonlinear control in, Communications Theoretical Physics, 55, 274. ; CHEN (1999), Yet another chaotic attractor of Bifurcation and, International Journal Chaos, 7, 1465, doi.org/10.1142/S0218127499001024 ; SAMPATH (2016), Hybrid synchronization of identical chaotic systems via novel sliding control method with application to Sampath four - scroll chaotic system of Control Theory and Applications, International Journal, 89, 221. ; VAIDYANATHAN (2016), Anti - synchronization of identical chaotic systems via novel sliding control method with application to Vaidyanathan - Madhavan chaotic system of Control Theory and Applications, International Journal, 88, 85. ; VAIDYANATHAN (2012), Anti - synchronization of four - wing chaotic systems via sliding mode control of Automatic, International Journal Computing, 86, 274. ; ARNEODO (1981), Possible new strange attractors with spiral structure in, Communications Mathematical Physics, 5, 573, doi.org/10.1007/BF01209312 ; VAIDYANATHAN (2013), A new six - term chaotic system with an exponential nonlinearity of Mathematical, Far East Journal Sciences, 15, 135. ; CHEN (2006), Generating hyperchaotic Lü attractor via state feedback control, Physica A, 54, 103, doi.org/10.1016/j.physa.2005.09.039 ; VAIDYANATHAN (2016), An eleven - term novel hyperchaotic system with three quadratic nonlinearities analysis control and synchronization via adaptive control method of Control Theory and Applications, International Journal, 68, 21. ; TAN (2003), Synchronizing chaotic systems using backstepping design Solitons and, Chaos Fractals, 80, 37, doi.org/10.1016/S0960-0779(02)00153-4 ; RÖSSLER (1976), An equation for continuous chaos, Physics Letters A, 4, 397, doi.org/10.1016/0375-9601(76)90101-8 ; CAI (2007), Adaptive backstepping control of the uncertain unified chaotic system of Nonlinear, International Journal Science, 72, 17. ; VAIDYANATHAN (2016), A highly chaotic system with four quadratic nonlinearities its analysis control and synchronization via integral sliding mode control of Control Theory and Applications, International Journal, 33, 279. ; VAIDYANATHAN (2011), Hybrid synchronization of hyperchaotic Wang and hyperchaotic lorenz systems by active non - linear control of Signal System Control and Engineering Application, International Journal, 76, 55. ; LÜ (2002), A new chaotic attractor coined of Bifurcation and, International Journal Chaos, 8, 659, doi.org/10.1142/S0218127402004620 ; VAIDYANATHAN (2013), A ten - term novel hyperchaotic system with three quadratic nonlinearities and its control of Control Theory and Applications, International Journal, 59, 97. ; SUNDARAPANDIAN (2011), Sliding controller design of hybrid synchronization of four - wing chaotic systems of, International Journal Soft Computing, 84, 224, doi.org/10.3923/ijscomp.2011.224.231 ; AZAR (2015), Chaos Modeling and Control Systems Design Springer, Berlin, 1. ; SUNDARAPANDIAN (2012), Adaptive anti - synchronization of Uncertain Tigan and Li Systems and, Journal of Engineering Applied Sciences, 79, 45. ; SPROTT (1994), Some simple chaotic flows, Physical Review E, 50, 647, doi.org/10.1103/PhysRevE.50.R647 ; VAIDYANATHAN (2014), Generalised projective synchronisation of novel chaotic systems with an exponential non - linearity via active and adaptive control of Modelling Identification and Control, International Journal, 22, 207. ; VAIDYANATHAN (2016), Analysis control synchronization and LabVIEW implementation of a seven - term novel chaotic system of Control Theory and Applications, International Journal, 31, 151. ; VAIDYANATHAN (2014), Analysis control and synchronisation of a six - term novel chaotic system with three quadratic nonlinearities of Modelling Identification and Control, International Journal, 18, 41. ; CHIEN (2005), Design of secure digital communication systems using chaotic modulation cryptography and chaotic synchronization Solitons, Chaos Fractals, 46, 241, doi.org/10.1016/S0960-0779(04)00542-9 ; PHAM (2016), A chaotic system with different families of hidden attractors of Bifurcation and, International Journal Chaos, 39, 1650139, doi.org/10.1142/S021812741650139X ; VAIDYANATHAN (2014), Qualitative analysis and control of an eleven - term novel hyperchaotic system with two quadratic nonlinearities of Control Theory and Applications, International Journal, 61, 35. ; VAIDYANATHAN (2016), A novel conservative chaotic system with a sinusoidal nonlinearity and its adaptive control of Control Theory and Applications, International Journal, 29, 115. ; VAIDYANATHAN (2014), Global chaos synchronisation of identical Li - Wu chaotic systems via sliding mode control of Modelling Identification and Control, International Journal, 87, 170. ; TIGAN (2008), Analysis of a chaotic system Solitons and, Chaos Fractals, 11, 1315, doi.org/10.1016/j.chaos.2006.07.052 ; VAIDYANATHAN (2016), A five - term novel conservative chaotic system and its generalized projective synchronization via adaptive control method of Control Theory and Applications, International Journal, 28, 61. ; ZHANG (2013), A novel image fusion encryption algorithm based on DNA sequence operation and hyper - chaotic system, Optik, 48, 3596, doi.org/10.1016/j.ijleo.2012.11.018 ; VAIDYANATHAN (2014), A new eight - term polynomial chaotic system with three quadratic nonlinearities of Mathematical, Far East Journal Sciences, 17, 219. ; CAI (2007), Chaos synchronization of a new chaotic system via nonlinear control of Uncertain Systems, Journal, 10, 235. ; VAIDYANATHAN (2015), Analysis and control of a novel hyperchaotic system in, Studies Computational Intelligence, 62, 3. ; YUJUN (2010), A new hyperchaotic system and its circuit implementation in and Numerical Simulation, Communications Nonlinear Science, 51, 3518, doi.org/10.1016/j.cnsns.2009.12.005 ; PHAM (2016), A novel memristive neural network with hidden attractors and its circuitry implementation China Technological, Science Sciences, 38, 358. ; VAIDYANATHAN (2015), novel highly chaotic system with four quadratic nonlinearities its adaptive control and anti - synchronization with unknown parameters of and Technology, Journal Engineering Science Review, 25, 106. ; LAOYE (2009), Chaos control of chaotic systems using recursive backstepping nonlinear controller Solitons and, Chaos Fractals, 74, 356, doi.org/10.1016/j.chaos.2007.04.020 ; LIU (2004), A new chaotic attractor Solitons and, Chaos Fractals, 9, 1031, doi.org/10.1016/j.chaos.2004.02.060 ; RASAPPAN (2013), Hybrid synchronization ofn - scroll Chua circuits using adaptive backstepping control design with recursive feedback of Mathematical, Malaysian Journal Sciences, 83, 219. ; WANG (2008), A novel hyperchaotic system and its complex dynamics of Bifurcation and, International Journal Chaos, 56, 3309, doi.org/10.1142/S0218127408022391 ; SMAOUI (2011), Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems in and Numerical Simulation, Communications Nonlinear Science, 45, 3279, doi.org/10.1016/j.cnsns.2010.10.023 ; VAIDYANATHAN (2015), Analysis control and synchronization of a novel jerk chaotic system with two quadratic nonlinearities Mathematical, Kyungpook Journal, 26, 563, doi.org/10.5666/KMJ.2015.55.3.563 ; VAIDYANATHAN (2012), Global chaos control of hyperchaotic Liu system via sliding control method of Control Theory and Applications, International Journal, 85, 117. ; PHAM (2016), A no - equilibrium hyperchaotic system with a cubic nonlinear term, Optik, 69, 3259, doi.org/10.1016/j.ijleo.2015.12.048 ; RASAPPAN (2012), Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control of Mathematical, Far East Journal Sciences, 81, 265. ; VAIDYANATHAN (2013), Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters of and Technology, Journal Engineering Science Review, 16, 53. ; VAIDYANATHAN (2016), A novel hyperchaotic system with two quadratic nonlinearities its analysis and synchronization via integral sliding mode control of Control Theory and Applications, International Journal, 67, 321. ; ZHANG (2006), Chaotic secure communication based on particle filtering Solitons, Chaos Fractals, 47, 1273, doi.org/10.1016/j.chaos.2005.09.019 ; RASAPPAN (2012), Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback in Computer and Information, Communications Science, 82, 212. ; VAIDYANATHAN (2016), Analysis and adaptive control of a novel conservative no - equilibrium chaotic system of Control, Archives Sciences, 23, 333. ; VAIDYANATHAN (2016), Advances and Applications in Chaotic Systems Springer, Berlin, 2. ; VAIDYANATHAN (2016), Adaptive control and synchronization design of a seven - term novel chaotic system with a quartic nonlinearity of Control Theory and Applications, International Journal, 32, 237. ; VAIDYANATHAN (2013), Analysis adaptive control and synchronization of a seven - term novel chaotic system of Control Theory and Applications, International Journal, 19, 121. ; BUSCARINO (2009), Experimental robust synchronization of hyperchaotic circuits : Nonlinear, Physica D Phenomena, 50, 1917, doi.org/10.1016/j.physd.2009.06.021 ; VAIDYANATHAN (2012), Adaptive backstepping controller and synchronizer design for Arneodo chaotic system with unknown parameters of and Information Technology, International Journal Computer Science, 75, 145. ; VAIDYANATHAN (2014), Hyperchaos adaptive control and synchronization of a novel hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation of Control, Archives Sciences, 60, 409. ; PEHLIVAN (2014), Analysis synchronization and circuit design of a novel butterfly attractor and, Journal of Sound Vibration, 35, 5077, doi.org/10.1016/j.jsv.2014.05.025 ; AKGUL (2016), A new four - scroll chaotic attractor and its engineering applications, Optik, 42, 5491, doi.org/10.1016/j.ijleo.2016.02.066 ; LI (2008), A three - scroll chaotic attractor, Physics Letters A, 12, 387, doi.org/10.1016/j.physleta.2007.07.045 ; JAFARI (2013), Simple chaotic flows with a line equilibrium Solitons and, Chaos Fractals, 36, 79, doi.org/10.1016/j.chaos.2013.08.018 ; SAMPATH (2015), An eight - term novel four - scroll chaotic system with cubic nonlinearity and its circuit simulation of and Technology, Journal Engineering Science Review, 41, 1. ; KARTHIKEYAN (2014), Hybrid chaos synchronization of four - scroll systems via active control of, Journal Electrical Engineering, 77, 97. ; SAMPATH (2016), A novel hyperchaotic system with three quadratic nonlinearities its adaptive control and circuit simulation of Control Theory and Applications, International Journal, 70, 339. ; GHOSH (2010), Projective synchronization of new hyperchaotic system with fully unknown parameters, Nonlinear Dynamics, 57, 11, doi.org/10.1007/s11071-009-9627-4 ; JIA (2007), Hyperchaos generated from the Lorenz chaotic system and its control, Physics Letters A, 53, 217, doi.org/10.1016/j.physleta.2007.02.024 ; VAIDYANATHAN (2015), Analysis properties and control of an eight - term chaotic system with an exponential nonlinearity of Modelling Identification and Control, International Journal, 24, 164.