Synchronization of different fractional order chaotic systems using active control

Communications in Nonlinear Science and Numerical Simulation - Tập 15 Số 11 - Trang 3536-3546 - 2010
Sachin Bhalekar1, Varsha Daftardar-Gejji1
1Department of Mathematics, University of Pune, Ganeshkhind, Pune 411007, India

Tóm tắt

Từ khóa


Tài liệu tham khảo

Pecora, 1990, Synchronization in chaotic systems, Phys Rev Lett, 64, 821, 10.1103/PhysRevLett.64.821

Pecora, 1991, Driving systems with chaotic signals, Phys Rev A, 44, 2374, 10.1103/PhysRevA.44.2374

Kocarev, 1995, General approach for chaotic synchronization with applications to communication, Phys Rev Lett, 74, 5028, 10.1103/PhysRevLett.74.5028

Carroll, 1996, Transforming signals with chaotic synchronization, Phys Rev E, 54, 4676, 10.1103/PhysRevE.54.4676

Hilfer, 2001

He, 1998, Implementation of chaotic cryptography with chaotic synchronization, Phys Rev E, 57, 1532, 10.1103/PhysRevE.57.1532

Huang, 2004, Synchronization of chaotic systems via nonlinear control, Phys Lett A, 320, 271, 10.1016/j.physleta.2003.11.027

Liao, 1998, Adaptive synchronization of two Lorenz systems, Chaos Solitons Fractals, 9, 1555, 10.1016/S0960-0779(97)00161-6

Yassen, 2001, Adaptive control and synchronization of a modified Chua’s circuit system, Appl Math Comput, 135, 113, 10.1016/S0096-3003(01)00318-6

Wang, 2004, Adaptive synchronization for Chen chaotic system with fully unknown parameters, Chaos Solitons Fractals, 19, 899, 10.1016/S0960-0779(03)00256-X

Park, 2005, Adaptive synchronization of Rossler system with uncertain parameters, Chaos Solitons Fractals, 25, 333, 10.1016/j.chaos.2004.12.007

Bowong, 2004, Synchronization of uncertain chaotic systems via backstepping approach, Chaos Solitons Fractals, 21, 999, 10.1016/j.chaos.2003.12.084

Zhang, 2004, Chaos synchronization using single variable feedback based on backstepping method, Chaos Solitons Fractals, 21, 1183, 10.1016/j.chaos.2003.12.079

Bai, 1997, Synchronization of two Lorenz systems using active control, Chaos Solitons Fractals, 8, 51, 10.1016/S0960-0779(96)00060-4

Bai, 2000, Sequential synchronization of two Lorenz systems using active control, Chaos Solitons Fractals, 11, 1041, 10.1016/S0960-0779(98)00328-2

Agiza, 2001, Synchronization of Rossler and chaotic dynamical systems using active control, Phys Lett A, 278, 191, 10.1016/S0375-9601(00)00777-5

Ho, 2002, Synchronization of two different systems by using generalized active control, Phys Lett A, 301, 424, 10.1016/S0375-9601(02)00987-8

Codreanu, 2003, Synchronization of spatiotemporal nonlinear dynamical systems by an active control, Chaos Solitons Fractals, 15, 507, 10.1016/S0960-0779(02)00128-5

Zhang, 2004, Synchronization of uncertain chaotic systems with parameters perturbation via active control, Chaos Solitons Fractals, 21, 39, 10.1016/j.chaos.2003.09.014

Ucar, 2004, Synchronization of the coupled FitzHugh0Nagumo systems, Chaos Solitons Fractals, 20, 1085, 10.1016/j.chaos.2003.09.039

Yassen, 2005, Chaos synchronization between two different chaotic systems using active control, Chaos Solitons Fractals, 23, 131, 10.1016/j.chaos.2004.03.038

Lei, 2006, Global synchronization of two parametrically excited systems using active control, Chaos Solitons Fractals, 28, 428, 10.1016/j.chaos.2005.05.043

Wu, 2009, Synchronization of a new fractional order hyperchaotic system, Phys Lett A, 373, 2329, 10.1016/j.physleta.2009.04.063

Shahiri, 2010, Chaotic fractional-order Coullet system: synchronization and control approach, Commun Nonlinear Sci Numer Simulat, 15, 665, 10.1016/j.cnsns.2009.05.054

Podlubny, 1999

Samko, 1993

Kilbas, 2006

Sabatier, 2004, Robust speed control of a low damped electromechanical system based on CRONE control: application to a four mass experimental test bench, Nonlinear Dyn, 38, 383, 10.1007/s11071-004-3768-2

Caputo, 1971, A new dissipation model based on memory mechanism, Pure Appl Geophys, 91, 134, 10.1007/BF00879562

Mainardi, 2001, The fundamental solution of the space-time fractional diffusion equation, Fractional Calculus Appl Anal, 4, 153

Agrawal, 2002, Solution for a fractional diffusion-wave equation defined in a bounded domain, Nonlinear Dyn, 29, 145, 10.1023/A:1016539022492

Daftardar-Gejji, 2006, Boundary value problems for fractional diffusion-wave equations, Aust J Math Anal Appl, 3, 1

Daftardar-Gejji, 2008, Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method, Appl Math Comput, 202, 113, 10.1016/j.amc.2008.01.027

Sun, 2009, Variable-order fractional differential operators in anomalous diffusion modeling, Physica A, 388, 4586, 10.1016/j.physa.2009.07.024

Jesus, 2008, Fractional control of heat diffusion systems, Nonlinear Dyn, 54, 263, 10.1007/s11071-007-9322-2

Jesus IS, Machado JAT, Barbosa RS. Control of a heat diffusion system through a fractional order nonlinear algorithm. Comput Math Appl, in press. doi: 10.1016/j.camwa.2009.08.010.

Anastasio, 1994, The fractional-order dynamics of brainstem vestibulo-oculomotor neurons, Biol Cybern, 72, 69, 10.1007/BF00206239

Ortigueira, 2006, Fractional calculus applications in signals and systems, Signal Process, 86, 2503, 10.1016/j.sigpro.2006.02.001

Magin, 2006

Daftardar-Gejji, 2004, Analysis of a system of fractional differential equations, J Math Appl Anal, 293, 511, 10.1016/j.jmaa.2004.01.013

Daftardar-Gejji, 2007, Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives, J Math Appl Anal, 328, 1026, 10.1016/j.jmaa.2006.06.007

Matignon D. Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems and application multiconference, IMACS, IEEE-SMC proceedings, Lille, France, July, vol. 2; 1996. p. 963–8.

Kiani-B, 2009, A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter, Commun Nonlinear Sci Numer Simulat, 14, 863, 10.1016/j.cnsns.2007.11.011

Grigorenko, 2003, Chaotic dynamics of the fractional Lorenz system, Phys Rev Lett, 91, 034101, 10.1103/PhysRevLett.91.034101

Li, 2004, Chaos in Chens system with a fractional order, Chaos Solitons Fractals, 22, 443, 10.1016/j.chaos.2004.02.013

Lü, 2006, Chaotic dynamics of the fractional order Lü system and its synchronization, Phys Lett A, 354, 305, 10.1016/j.physleta.2006.01.068

Li, 2004, Chaos and hyperchaos in the fractional order Rossler equations, Phys A Stat Mech Appl, 341, 55, 10.1016/j.physa.2004.04.113

Daftardar-Gejji V, Bhalekar S. Chaos in fractional ordered Liu system. Comput Math Appl, in press. doi: 10.1016/j.camwa.2009.07.003.

Bhalekar, 2010, Fractional ordered Liu system with time-delay, Commun Nonlinear Sci Numer Simulat, 15, 2178, 10.1016/j.cnsns.2009.08.015

Deng, 2005, Chaos synchronization of the fractional Lü system, Physica A, 353, 61, 10.1016/j.physa.2005.01.021

Deng, 2005, Synchronization of chaotic fractional Chen system, J Phys Soc Jpn, 74, 1645, 10.1143/JPSJ.74.1645

Zhou, 2005, Synchronization in fractional-order differential systems, Physica D, 212, 111, 10.1016/j.physd.2005.09.012

Lia, 2006, Chaos synchronization of the Chua system with a fractional order, Physica A, 360, 171, 10.1016/j.physa.2005.06.078

Wang, 2006, Extending synchronization scheme to chaotic fractional-order Chen systems, Physica A, 370, 279, 10.1016/j.physa.2006.03.021

Wang, 2006, Designing synchronization schemes for chaotic fractional-order unified systems, Chaos Solitons Fractals, 30, 1265, 10.1016/j.chaos.2005.09.027

Xingyuan, 2008, Projective synchronization of fractional order chaotic system based on linear separation, Phys Lett A, 372, 435, 10.1016/j.physleta.2007.07.053

Yu, 2008, The synchronization of fractional-order Rossler hyperchaotic systems, Physica A, 387, 1393, 10.1016/j.physa.2007.10.052

Tavazoei, 2008, Synchronization of chaotic fractional-order systems via active sliding mode controller, Physica A, 387, 57, 10.1016/j.physa.2007.08.039

Matouk, 2009, Chaos synchronization between two different fractional systems of Lorenz family, Math Prob Eng, 2009, 10.1155/2009/572724

Hu, 2010, Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems, Commun Nonlinear Sci Numer Simulat, 15, 115, 10.1016/j.cnsns.2009.03.017

Luchko, 1999, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math Vietnamica, 24, 207

Diethelm, 2002, A predictor–corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn, 29, 3, 10.1023/A:1016592219341

Diethelm, 1997, An algorithm for the numerical solution of differential equations of fractional order, Elec Trans Numer Anal, 5, 1

Diethelm, 2002, Analysis of fractional differential equations, J Math Anal Appl, 265, 229, 10.1006/jmaa.2000.7194

Wu, 2009, Chaos in the fractional-order Lorenz system, Int J Comput Math, 86, 1274, 10.1080/00207160701864426

Liu, 2009, A novel three-dimensional autonomous chaos system, Chaos Solitons Fractals, 39, 1950, 10.1016/j.chaos.2007.06.079

Tavazoei, 2008, Chaotic attractors in incommensurate fractional order systems, Physica D, 237, 2628, 10.1016/j.physd.2008.03.037

Tavazoei, 2007, A necessary condition for double scroll attractor existence in fractional order systems, Phys Lett A, 367, 102, 10.1016/j.physleta.2007.05.081