Title

Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

Journal title

Archives of Control Sciences

Yearbook

2016

Issue

No 4

Authors

Sundarapandian Vaidyanathan

Divisions of PAS

Nauki Techniczne

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

DOI: 10.1515/acsc-2016-0026 ; ISSN 1230-2384

Source

Archives of Control Sciences; 2016; No 4

References

VOLOS (2016), Synchronization and anti - synchronization of coupled Hindmarsh - Rose neuron models of Control Theory and Applications, International Journal, 46, 101. ; WEI (2012), A novel four - wing hyper - chaotic system and its circuit implementation, Procedia Engineering, 63, 1264, doi.org/10.1016/j.proeng.2012.01.124 ; YE (2014), A block chaotic image encryption scheme based on selfadaptive modelling, Applied Soft Computing, 59, 351, doi.org/10.1016/j.asoc.2014.05.025 ; VAIDYANATHAN (2013), A new six - term chaotic system with an exponential nonlinearity of Mathematical, Far East Journal Sciences, 79, 135. ; TACHA (2016), Analysis adaptive control and circuit simulation of a novel nonlinear finance system and, Applied Mathematics Computation, 32, 276. ; GASPARD (1999), Microscopic chaos and chemical reactions A : and its, Physica Statistical Mechanics Applications, 35, 263. ; CHEN (2006), Generating hyperchaotic Lü attractor via state feedback control, Physica A, 67, 364. ; VAIDYANATHAN (2013), Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters of and, Journal Engineering Science Technology Review, 6, 53. ; YUJUN (2010), A new hyperchaotic system and its circuit implementation in and Numerical, Communications Nonlinear Science Simulation, 62, 3518, doi.org/10.1016/j.cnsns.2009.12.005 ; RUELLE (1971), On the nature of turbulence in, Communications Mathematical Physics, 20, 167, doi.org/10.1007/BF01646553 ; VAIDYANATHAN (2015), Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method of PharmTech Research, International Journal, 34, 106. ; LI (2004), Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov - Zhabotinsky reaction Solitons, Chaos Fractals, 36, 195, doi.org/10.1016/S0960-0779(03)00103-6 ; VAIDYANATHAN (2015), Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control of, International Journal ChemTech Research, 44, 818. ; FEIGENBAUM (1983), Universal behaviour in nonlinear systems :, Physica D Nonlinear Phenomena, 7, 16, doi.org/10.1016/0167-2789(83)90112-4 ; GHOSH (2010), Projective synchronization of new hyperchaotic system with fully unknown parameters, Nonlinear Dynamics, 70, 11, doi.org/10.1007/s11071-009-9627-4 ; LIU (2004), A new chaotic attractor Solitons and, Chaos Fractals, 22, 1031, doi.org/10.1016/j.chaos.2004.02.060 ; WANG (2008), A novel hyperchaotic system and its complex dynamics of Bifurcation and, International Journal Chaos, 69, 3309, doi.org/10.1142/S0218127408022391 ; VAIDYANATHAN (2013), Analysis adaptive control and synchronization of a seven - term novel chaotic system of Control Theory and Applications, International Journal, 6, 121. ; LI (2005), Lag synchronization of hyperchaos with application to secure communications Solitons and, Chaos Fractals, 52, 183, doi.org/10.1016/j.chaos.2004.04.025 ; VAIDYANATHAN (2015), Global chaos synchronization of - cells cellular neural network attractors via integral sliding mode control of PharmTech Research, International Journal, 42, 118. ; SMAOUI (2011), Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems in and Numerical, Communications Nonlinear Science Simulation, 53, 3279, doi.org/10.1016/j.cnsns.2010.10.023 ; LI (2008), A three - scroll chaotic attractor, Physics Letters A, 372. ; CAI (2007), Chaos synchronization of a new chaotic system via nonlinear control of Uncertain Systems, Journal, 1, 235. ; LIU (2013), Color image encryption using Choquet fuzzy integral and hyper chaotic system - for Light and, Optik International Journal Electron Optics, 60, 3257. ; ZHANG (2013), A novel image fusion encryption algorithm based on DNA sequence operation and hyper - chaotic system - for Light and, Optik International Journal Electron Optics, 58, 3596, doi.org/10.1016/j.ijleo.2012.11.018 ; TIGAN (2008), Analysis of a D chaotic system Solitons and, Chaos Fractals, 36, 1315, doi.org/10.1016/j.chaos.2006.07.052 ; VAIDYANATHAN (2014), Analysis control and synchronisation of a six - term novel chaotic system with three quadratic nonlinearities of Modelling , Identification and Control, International Journal, 22, 41. ; VAIDYANATHAN (2014), A new eight - term polynomial chaotic system with three quadratic nonlinearities of Mathematical, Far East Journal Sciences, 84, 219. ; SUNDARAPANDIAN (2012), Analysis control , synchronization and circuit design of a novel chaotic system and, Mathematical Computer Modelling, 55, 1904, doi.org/10.1016/j.mcm.2011.11.048 ; VAIDYANATHAN (null), Advances and Applications in Nonlinear Control Systems Springer -, Berlin Verlag, 2016. ; SPROTT (2010), Elegant Chaos World Scientific, Singapore, 51. ; PHAM (2016), A no - equilibrium hyperchaotic system with a cubic nonlinear term, Optik, 127, 3259, doi.org/10.1016/j.ijleo.2015.12.048 ; PHAM (2016), A chaotic system with infinite equilibria located on a piecewise linear curve, Optik, 127, 9111, doi.org/10.1016/j.ijleo.2016.06.111 ; VAIDYANATHAN (2011), Hybrid synchronization of hyperchaotic Qi and Lü systems by nonlinear control in Computer and Information, Communications Science, 74, 585. ; BUSCARINO (2009), Experimental robust synchronization of hyperchaotic circuits :, Physica D Nonlinear Phenomena, 61, 238. ; CHIEN (2005), Design of secure digital communication systems using chaotic modulation , cryptography and chaotic synchronization Solitons, Chaos Fractals, 55, 241, doi.org/10.1016/S0960-0779(04)00542-9 ; ARNEODO (1981), Possible new strange attractors with spiral structure in, Communications Mathematical Physics, 79, 573, doi.org/10.1007/BF01209312 ; VAIDYANATHAN (2012), Adaptive controller and synchronizer design for the Qi - chaotic system Notes of the Institute for Computer Social - Informatics and Telecommunications, Chen Lecture Sciences Engineering, 73, 124. ; VAIDYANATHAN (2015), Adaptive backstepping controller design for the anti - synchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementation of and, Journal Engineering Science Technology Review, 49, 74. ; SPROTT (2005), Coexistence and chaos in complex ecologies, Physics Letters A, 40, 335. ; VAIDYANATHAN (null), Advances and Applications in Chaotic Systems Springer -, Berlin Verlag, 1, 2016. ; LÜ (2002), A new chaotic attractor coined of Bifurcation and, International Journal Chaos, 12, 659, doi.org/10.1142/S0218127402004620 ; VAIDYANATHAN (2015), Global chaos control of - cells cellular neural network attractor via integral sliding mode control of PharmTech Research, International Journal, 41, 211. ; LI (2009), Modified projective synchronization of a new hyperchaotic system via nonlinear control in, Communications Theoretical Physics, 68, 274. ; WU (2011), Hyperchaotic secure communication via generalized function projective synchronization Analysis : Real, Nonlinear World Applications, 54, 1288, doi.org/10.1016/j.nonrwa.2010.09.026 ; PHAM (2016), A chaotic system with different families of hidden attractors of Bifurcation and, International Journal Chaos, 26, 1650139, doi.org/10.1142/S021812741650139X ; SUÁREZ (1999), Mastering chaos in ecology, Ecological Modelling, 39, 305, doi.org/10.1016/S0304-3800(99)00007-1 ; VAIDYANATHAN (2016), Global chaos control of the FitzHugh - Nagumo chaotic neuron model via integral sliding mode control of PharmTech Research, International Journal, 47, 413. ; VAIDYANATHAN (2014), Adaptive backstepping control , synchronization and circuit simulation of a novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities of Control, Archives Sciences, 24, 257. ; SPROTT (1994), Some simple chaotic flows, Physical Review E, 50, 647, doi.org/10.1103/PhysRevE.50.R647 ; LORENZ (1963), Deterministic nonperiodic flow of the, Journal Atmospheric Sciences, 20, 130, doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 ; CHEN (1999), Yet another chaotic attractor of Bifurcation and, International Journal Chaos, 9, 1465, doi.org/10.1142/S0218127499001024 ; JAFARI (2013), Simple chaotic flows with a line equilibrium Solitons and, Chaos Fractals, 57, 79, doi.org/10.1016/j.chaos.2013.08.018 ; PEHLIVAN (2014), Analysis synchronization and circuit design of a novel butterfly attractor of and, Journal Sound Vibration, 25, 333. ; ZHOU (2014), A new non - equilibrium fractional - order chaotic system and its circuit implementation in and Numerical, Communications Nonlinear Science Simulation, 64, 4. ; RÖSSLER (1976), An equation for continuous chaos, Physics Letters A, 57, 397, doi.org/10.1016/0375-9601(76)90101-8 ; RÖSSLER (1979), An equation for hyperchaos, Physics Letters A, 65, 155, doi.org/10.1016/0375-9601(79)90150-6 ; ZHANG (2006), Chaotic secure communication based on particle filtering Solitons, Chaos Fractals, 56, 1273, doi.org/10.1016/j.chaos.2005.09.019 ; VOLOS (2015), Synchronization phenomena in coupled Colpitts circuits of and, Journal Engineering Science Technology Review, 50, 142. ; SUNDARAPANDIAN (2013), Analysis and anti - synchronization of a novel chaotic system via active and adaptive controllers of and, Journal Engineering Science Technology Review, 6, 45. ; VAIDYANATHAN (2015), Adaptive synchronization of the identical FitzHugh - Nagumo chaotic neuron models of PharmTech Research, International Journal, 48, 167. ; PHAM (2016), A chaotic system with equilibria located on the rounded square loop and its circuit implementation on Circuits and Systems - II :, IEEE Transactions Express Briefs, 31, 878. ; VAIDYANATHAN (2016), Global chaos regulation of a symmetric nonlinear gyro system via integral sliding mode control of, International Journal ChemTech Research, 43, 462. ; CARLEN (2013), Kinetic hierarchy and propagation of chaos in biological swarm models :, Physica D Nonlinear Phenomena, 38, 260. ; VAIDYANATHAN (2015), Dynamics and control of Tokamak system with symmetric and magnetically confined plasma of, International Journal ChemTech Research, 45, 795. ; MAY (1972), Limit cycles in predator - prey communities, Science, 177. ; KYRIAZIS (1991), Applications of chaos theory to the molecular biology of aging, Experimental Gerontology, 37, 569, doi.org/10.1016/0531-5565(91)90074-V ; JIA (2007), Hyperchaos generated from the Lorenz chaotic system and its control, Physics Letters A, 66, 366. ; AKGUL (2016), A new fourscroll chaotic attractor and its engineering applications, Optik, 127, 5491, doi.org/10.1016/j.ijleo.2016.02.066 ; WU (2014), A new color image cryptosystem via hyperchaos synchronization in and Numerical, Communications Nonlinear Science Simulation, 57, 1884, doi.org/10.1016/j.cnsns.2013.10.025 ; VAIDYANATHAN (2014), Analysis and adaptive synchronization of eight - term polynomial chaotic systems with three quadratic nonlinearities :, European Physical Journal Special Topics, 223. ; PHAM (2015), Multi - scroll chaotic oscillator based on a first - order delay differential equation in, Studies Computational Intelligence, 33, 581.