Szczegóły

Tytuł artykułu

A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

Tytuł czasopisma

Archives of Control Sciences

Rocznik

2016

Numer

No 1

Autorzy publikacji

Wydział PAN

Nauki Techniczne

Abstrakt

<jats:p>This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L<jats:sub>1</jats:sub> = 0.20572,L<jats:sub>2</jats:sub> = 0 and L<jats:sub>3</jats:sub> = −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as D<jats:sub>KY</jats:sub> = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.</jats:p>

Wydawca

Committee of Automatic Control and Robotics PAS

Data

2016

Identyfikator

ISSN 1230-2384

Referencje

VAIDYANATHAN (2015), Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method of PharmTech Research, International Journal, 43, 106. ; VAIDYANATHAN (2014), A new eight - term polynomial chaotic system with three quadratic nonlinearities of, Far East Journal Mathematical Sciences, 17, 219. ; VAIDYANATHAN (2015), Analysis adaptive control and synchronization of a seventerm novel chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW of and, Journal Engineering Science Technology Review, 25, 130. ; VAIDYANATHAN (2015), Anti - synchronization of chemical chaotic reactors via adaptive control method of, International Journal ChemTech Research, 53, 73. ; VAIDYANATHAN (2015), Adaptive backstepping controller design for the antisynchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementation of and, Journal Engineering Science Technology Review, 110, 74. ; VAIDYANATHAN (2015), Global chaos synchronization of novel coupled Van der Pol conservative chaotic systems via adaptive control method of PharmTech Research, International Journal, 40, 95. ; SUNDARAPANDIAN (2012), Analysis control , synchronization and circuit design of a novel chaotic system and Computer Modelling, Mathematical, 13, 1904. ; VAIDYANATHAN (2011), Output regulation of the unified chaotic system in Computer and, Communications Information Science, 96, 1. ; VOLOS (2015), Random bit generator based on non - autonomous chaotic systems of Research on Advanced Intelligent Control Engineering and Automation, Handbook, 92, 203. ; VAIDYANATHAN (2012), Anti - synchronization of four - wing chaotic systems via sliding mode control of Automation and Computing, International Journal, 117, 274. ; VAIDYANATHAN (2012), Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control of, International Journal Soft Computing, 102, 28, doi.org/10.3923/ijscomp.2012.28.37 ; VAIDYANATHAN (2015), novel highly chaotic system with four quadratic nonlinearities , its adaptive control and anti - synchronization with unknown parameters of and, Journal Engineering Science Technology Review, 24, 106. ; VAIDYANATHAN (2015), Hyperchaos qualitative analysis , control and synchronisation of a ten - term hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities of Modelling , Identification and Control, International Journal, 103, 380. ; VOLOS (2015), Synchronization phenomena in coupled Colpitts circuits of and, Journal Engineering Science Technology Review, 86, 142. ; VAIDYATHAN (2015), Global chaos synchronization of - cells cellular neural network attractors via integral sliding mode control of PharmTech Research, International Journal, 67, 118. ; VAIDYATHAN (2015), Sliding mode control of Rucklidge chaotic system for nonlinear double convection of, International Journal ChemTech Research, 83, 25. ; VAIDYANATHAN (2015), Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system of Modelling , Identification and Control, International Journal, 119, 92. ; VAIDYANATHAN (2015), Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method of, International Journal ChemTech Research, 55, 209. ; VAIDYANATHAN (2015), Analysis control , synchronization and SPICE implementation of a novel hyperchaotic Rikitake dynamo system without equilibrium of and, Journal Engineering Science Technology Review, 49, 232. ; VAIDYATHAN (2015), Hybrid chaos synchronization of - cells cellular neural network attractors via adaptive control method of PharmTech Research, International Journal, 64, 61. ; LÜ (2002), A new chaotic attractor coined of and, International Journal Bifurcation Chaos, 8, 659, doi.org/10.1142/S0218127402004620 ; VAIDYANATHAN (2015), Global chaos synchronization of Duffing double - well chaotic oscillators via integral sliding mode control of, International Journal ChemTech Research, 46, 141. ; PHAM (2015), Hidden attractors in a chaotic system with an exponential nonlinear term :, European Physical Journal Special Topics, 36, 1507, doi.org/10.1140/epjst/e2015-02476-9 ; VAIDYATHAN (2015), Adaptive backstepping control of enzymes - substrates system with ferroelectric behaviour in brain waves of PharmTech Research, International Journal, 70, 256. ; PHAM (2015), Chaotic attractor in a novel time - delayed system with a saturation function of Research on Advanced Intelligence Control Engineering and Automation, Handbook, 38, 230. ; HÉNON (1964), The applicability of the third integral of motion : Some numerical experiments, Astrophysical Journal, 7, 73. ; 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 ; 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), Global chaos synchronization of Mathieu - Van der Pol chaotic systems via adaptive control method of, International Journal ChemTech Research, 44, 148. ; LIU (2004), A new chaotic attractor Solitons and Fractals, Chaos, 9, 1031. ; VAIDYANATHAN (2015), Anti - synchronization of Rikitake two - disk dynamo chaotic systems via adaptive control method of, International Journal ChemTech Research, 48, 393. ; VAIDYATHAN (2015), Adaptive biological control of generalized Lotka - Volterra three - species biological system of PharmTech Research, International Journal, 79, 622. ; VAIDYANATHAN (2015), Backstepping controller design for the global chaos synchronization of Sprott s jerk systems in, Studies Computational Intelligence, 113, 39, doi.org/10.1007/978-3-319-13132-0_3 ; VAIDYANATHAN (2013), Analysis adaptive control and synchronization of a seven - term novel chaotic system of Control Theory and Applications, International Journal, 19, 121. ; 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 (2015), Analysis adaptive control and adaptive synchronization of a nine - term novel chaotic system with four quadratic nonlinearities and its circuit simulation of and, Journal Engineering Science Technology Review, 27, 174. ; SARASU (2012), Generalized projective synchronization of three - scroll chaotic systems via adaptive control of Scientific Research, European Journal, 107, 504. ; VAIDYATHAN (2015), Adaptive control of the FitzHugh - Nagumo chaotic neuron model of PharmTech Research, International Journal, 73, 117. ; VAIDYATHAN (2015), Chaos in neurons and adaptive control of Birkhoff - Shaw strange chaotic attractor of PharmTech Research, International Journal, 76, 956. ; VAIDYANATHAN (2015), Analysis and adaptive control of a novel conservative no - equilibrium chaotic system of Control, Archives Sciences, 28, 333. ; VAIDYATHAN (2015), Anti - synchronization of the generalized Lotka - Volterra three - species biological systems via adaptive control of PharmTech Research, International Journal, 81, 141. ; SARASU (2012), Generalized projective synchronization of three - scroll chaotic systems via adaptive control of Scientific Research, European Journal, 101, 504. ; 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, 16, 53. ; 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. ; VAIDYANATHAN (2011), Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control in Computer and, Communications Information Science, 95, 10, doi.org/10.1007/978-3-642-22555-0_2 ; KHALIL (null), Nonlinear Systems York, New, 120, 2002. ; CHEN (1999), Yet another chaotic attractor of and, International Journal Bifurcation Chaos, 6, 1465, doi.org/10.1142/S0218127499001024 ; VAIDYANATHAN (2015), Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control method of PharmTech Research, International Journal, 41, 156. ; MATOUK (2011), Chaos feedback control and synchronization of a fractionalorder modified autonomous Van der PolU Duffing circuit in and Numerical Simulation, Communications Nonlinear Science, 84, 975, doi.org/10.1016/j.cnsns.2010.04.027 ; SUNDARAPANDIAN (2011), Anti - synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control of Systems Signal Control and Engineering Application, International Journal, 100, 18. ; VAIDYANATHAN (2012), Global chaos control of hyperchaotic Liu system via sliding control method of Control Theory and Applications, International Journal, 118, 117. ; VAIDYANATHAN (2015), Adaptive backstepping controller design for the antisynchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementation of and, Journal Engineering Science Technology Review, 112, 74. ; VAIDYATHAN (2015), Global chaos control of - cells cellular neural network attractor via integral sliding mode control of PharmTech Research, International Journal, 66, 211. ; VAIDYATHAN (2015), Active control design for the hybrid chaos synchronization of the Lotka - Volterra biological systems with four competitive species of PharmTech Research, International Journal, 78, 30. ; SARASU (2012), Generalized projective synchronization of two - scroll systems via adaptive control of, International Journal Soft Computing, 106, 146, doi.org/10.3923/ijscomp.2012.146.156 ; VAIDYANATHAN (2013), A new six - term chaotic system with an exponential nonlinearity of, Far East Journal Mathematical Sciences, 15, 135. ; VAIDYANATHAN (2015), A novel chemical chaotic reactor system and its output regulation via integral sliding mode control of, International Journal ChemTech Research, 56, 669. ; VAIDYATHAN (2015), Anti - synchronization of - cells cellular neural network attractors via adaptive control method of PharmTech Research, International Journal, 68, 26. ; VAIDYANATHAN (2015), Adaptive synchronization of novel chemical chaotic reactor systems of, International Journal ChemTech Research, 61, 159. ; SUNDARAPANDIAN (2011), Sliding controller design of hybrid synchronization of four - wing chaotic systems of, International Journal Soft Computing, 115, 224, doi.org/10.3923/ijscomp.2011.224.231 ; VAIDYANATHAN (2015), Adaptive control of a chemical chaotic reactor of PharmTech Research, International Journal, 54, 377. ; VAIDYANATHAN (2015), Dynamics and control of Tokamak system with symmetric and magnetically confined plasma of, International Journal ChemTech Research, 52, 795. ; VAIDYANATHAN (2015), hyperchaotic Rikitake dynamo system with hidden attractors :, European Physical Journal Special Topics, 50, 1575. ; VAIDYANATHAN (2015), Analysis control , and synchronization of a novel jerk chaotic system with two quadratic nonlinearities Mathematical, Kyungpook Journal, 29, 563, doi.org/10.5666/KMJ.2015.55.3.563 ; VAIDYATHAN (2015), - cells cellular neural network ( CNN ) attractor and its adaptive biological control of PharmTech Research, International Journal, 63, 632. ; RASAPPAN (2012), Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback in Computer and, Communications Information Science, 108, 212, doi.org/10.1007/978-3-642-32112-2_26 ; VAIDYATHAN (2015), Sliding controller design for the global chaos synchronization of enzymes - substrates systems of PharmTech Research, International Journal, 71, 89. ; VAIDYATHAN (2015), Adaptive synchronization of the identical FitzHugh - Nagumo chaotic neuron models of PharmTech Research, International Journal, 74, 167. ; TIGAN (2008), Analysis of a D chaotic system Solitons and Fractals, Chaos, 11, 1315. ; PHAM (2014), Hidden hyperchaotic attractor in a novel simple memristive neural network and ,, Optoelectronics Advanced Materials Rapid Communications, 89, 1157. ; IDOWU (2009), Synchronization of chaos in nonidentical parametrically excited systems Solitons and Fractals, Chaos, 93, 2322. ; VAIDYANATHAN (2015), A novel chemical reactor system and its adaptive control of, International Journal ChemTech Research, 60, 146. ; LI (2008), A three - scroll chaotic attractor A, Physics Letters, 12, 387, doi.org/10.1016/j.physleta.2007.07.045 ; JAFARI (2013), Simple chaotic flows with a line equilibrium Solitons and Fractals, Chaos, 33, 79. ; ARNEODO (1981), Possible new strange attractors with spiral structure in, Communications Mathematical Physics, 4, 573, doi.org/10.1007/BF01209312 ; VAIDYANATHAN (2015), novel conservative chaotic system and its generalized projective synchronization via adaptive control of and, Journal Engineering Science Technology Review, 30, 52. ; VAIDYANATHAN (2015), Sliding controller design for the global chaos synchronization of forced Van der Pol chaotic oscillators of PharmTech Research, International Journal, 42, 100. ; VAIDYANATHAN (2015), Adaptive synchronization of Rikitake two - disk dynamo chaotic systems of, International Journal ChemTech Research, 47, 100. ; VAIDYANATHAN (2015), Adaptive synchronization of chemical chaotic reactors of, International Journal ChemTech Research, 59, 612. ; VAIDYANATHAN (2015), Anti - synchronization of Mathieu - Van der Pol chaotic systems via adaptive control method of, International Journal ChemTech Research, 39, 638. ; VAIDYANATHAN (2015), Adaptive control design for the anti - synchronization of novel chemical chaotic reactor systems of, International Journal ChemTech Research, 58, 654. ; VAIDYANATHAN (2015), Design and SPICE implementation of a - term novel hyperchaotic system and its synchronisation via active control of Modelling , Identification and Control, International Journal, 97, 12. ; PHAM (2016), A no - equilibrium hyperchaotic system with a cubic nonlinear term, Optik, 37, 3259, doi.org/10.1016/j.ijleo.2015.12.048 ; CAI (2007), Chaos synchronization of a new chaotic system via nonlinear control of Uncertain Systems, Journal, 10, 235. ; SUNDARAPANDIAN (2011), Anti - synchronization of Lü and Pan chaotic systems by adaptive nonlinear control of Scientific Research, European Journal, 98, 94. ; VAIDYANATHAN (2015), Integral sliding mode control design for the global chaos synchronization of identical novel chemical chaotic reactor systems of, International Journal ChemTech Research, 57, 684. ; RÖSSLER (1976), An equation for continuous chaos A, Physics Letters, 3, 397, doi.org/10.1016/0375-9601(76)90101-8 ; VOLOS (2015), Memristor A new concept in synchronization of coupled neuromorphic circuits of and, Journal Engineering Science Technology Review, 91, 157. ; VAIDYANATHAN (2015), Analysis adaptive control and synchronization of a novel hyperchaotic hyperjerk system and its SPICE implementation of Control, Archives Sciences, 111, 135. ; VAIDYANATHAN (2015), A novel coupled Van der Pol conservative chaotic system and its adaptive control of PharmTech Research, International Journal, 45, 79. ; VAIDYANATHAN (2011), Hybrid synchronization of hyperchaoticWang - Chen and hyperchaotic lorenz systems by active non - linear control of Signal System Control and Engineering Application, International Journal, 94, 55. ; SAMPATH (2015), An eightterm novel four - scroll chaotic system with cubic nonlinearity and its circuit simulation of and, Journal Engineering Science Technology Review, 34, 1. ; VAIDYANATHAN (2015), hyperchaotic Rikitake dynamo system with hidden attractors :, European Physical Journal Special Topics, 104, 1575, doi.org/10.1140/epjst/e2015-02481-0 ; VOLOS (2009), Experimental study of the dynamic behavior of a double scroll circuit of Applied Functional, Journal Analysis, 85, 703. ; VAIDYATHAN (2015), Active control design for the anti - synchronization of Lotka - Volterra biological systems with four competitive species of PharmTech Research, International Journal, 75, 58. ; PEHLIVAN (2014), Analysis synchronization and circuit design of a novel butterfly attractor of and, Journal Sound Vibration, 31, 5077, doi.org/10.1016/j.jsv.2014.05.025 ; PHAM (2014), Constructing a novel no - equilibrium chaotic system of and, International Journal Bifurcation Chaos, 35, 1450073, doi.org/10.1142/S0218127414500734 ; VAIDYANATHAN (2015), Anti - synchronization of Brusselator chemical reaction systems via adaptive control of, International Journal ChemTech Research, 62, 759. ; VAIDYATHAN (2015), Global chaos synchronization of the Lotka - Volterra biological systems with four competitive species via active control of PharmTech Research, International Journal, 77, 206. ; LORENZ (1963), Deterministic nonperiodic flow the, Journal of Atmospheric Sciences, 2, 130, doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 ; SPROTT (1994), Some simple chaotic flows, Physical Review E, 5, 647, doi.org/10.1103/PhysRevE.50.R647 ; VOLOS (2013), Text encryption scheme realized with a chaotic pseudo - random bit generator of and, Journal Engineering Science Technology Review, 88, 9. ; VAIDYATHAN (2015), Synchronization of - cells cellular neural network ( CNN ) attractors via adaptive control method of PharmTech Research, International Journal, 65, 946. ; VAIDYATHAN (2015), Adaptive synchronization of generalized Lotka - Volterra threespecies biological systems of PharmTech Research, International Journal, 80, 928. ; VAIDYANATHAN (2014), Global chaos synchronization of nscroll Chua circuit and Lur e system using backstepping control design with recursive feedback for and, Arabian Journal Science Engineering, 109, 3351, doi.org/10.1007/s13369-013-0929-y ; VAIDYATHAN (2015), Adaptive chaotic synchronization of enzymes - substrates system with ferroelectric behaviour in brain waves of PharmTech Research, International Journal, 69, 964. ; SUNDARAPANDIAN (2012), Adaptive antisynchronization of Uncertain Tigan and Li Systems of and, Journal Engineering Applied Sciences, 99, 45. ; PHAM (2015), A memristor - based hyperchaotic system with hidden attractors : Dynamics , synchronization and circuital emulating of and, Journal Engineering Science Technology Review, 90, 205. ; TACHA (2016), Analysis adaptive control and circuit simulation of a novel nonlinear finance system and, Applied Mathematics Computation, 32, 200, doi.org/10.1016/j.amc.2015.12.015 ; VAIDYANATHAN (2011), Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control in Computer and, Communications Information Science, 114, 156, doi.org/10.1007/978-3-642-24055-3_16 ; VOLOS (2013), Image encryption process based on chaotic synchronization phenomena, Signal Processing, 87, 1328, doi.org/10.1016/j.sigpro.2012.11.008 ; VAIDYANATHAN (2015), Analysis adaptive control and anti - synchronization of a sixterm novel jerk chaotic system with two exponential nonlinearities and its circuit simulation of and, Journal Engineering Science Technology Review, 26, 24. ; VAIDYANATHAN (2014), Global chaos synchronisation of identical Li - Wu chaotic systems via sliding mode control of Modelling , Identification and Control, International Journal, 116, 170. ; VAIDYATHAN (2015), Global chaos synchronization of Rucklidge chaotic systems for double convection via sliding mode control of, International Journal ChemTech Research, 82, 61. ; VAIDYATHAN (2015), Anti - synchronization of the FitzHugh - Nagumo chaotic neuron models via adaptive control method of PharmTech Research, International Journal, 72, 71. ; VAIDYANATHAN (2015), Analysis properties and control of an eight - term chaotic system with an exponential nonlinearity of Modelling , Identification and Control, International Journal, 23, 164. ; SUNDARAPANDIAN (2013), Analysis and anti - synchronization of a novel chaotic system via active and adaptive controllers of and, Journal Engineering Science Technology Review, 14, 45. ; VAIDYANATHAN (2015), Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control of, International Journal ChemTech Research, 51, 818.

DOI

10.1515/acsc-2016-0002

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