Fractional synchronization involving fractional derivatives with nonsingular kernels: Application to chaotic systems

被引:4
作者
Coronel-Escamilla, A. [1 ]
Gomez-Aguilar, J. F. [2 ,3 ]
Torres-Jimenez, J. [4 ]
Mousa, A. A. [5 ,6 ]
Elagan, S. K. [5 ,7 ]
机构
[1] Univ Texas San Antonio, Neurosci Inst, San Antonio, TX USA
[2] CONACyT Tecnol Nacl Mexico CENIDET, Interior Internado Palmira S-N, Cuernavaca 62490, Mexico
[3] Univ Virtual CNCI, Monterrey, Nuevo Leon, Mexico
[4] Tecnol Nacl Mexico, Inst Tecnol Super Huauchinango, Ingn Elect Maestria Tecnol Informac, Av Tecnol 80, Puebla, Mexico
[5] Taif Univ, Coll Sci, Dept Math & Stat, At Taif, Saudi Arabia
[6] Menoufia Univ, Fac Engn, Dept Basic Engn Sci, Shibin Al Kawm, Egypt
[7] Menoufia Univ, Dept Math, Fac Sci, Shibin Al Kawm, Egypt
关键词
fractional derivatives and integrals; fractional programming; COMPOUND SYNCHRONIZATION; ADAPTIVE-CONTROL; IDENTIFICATION; OBSERVER;
D O I
10.1002/mma.7315
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a novel master-slave fractional synchronization in chaotic systems by using fractional derivatives with nonlocal and nonsingular kernel. The master system is the fractional-order chaotic system, and then, we designed a fractional-order high gain observer, which is the slave system, based on the chaotic system model to achieve the synchronization. We used three different oscillator systems, a novel Chen-Burke-Shaw chaotic attractor, a novel fractional-order chaotic system, and the fractional-order model of a simple autonomous Jerk circuit. Our research followed to test the performance of the fractional synchronization. We use two performance indices, the integral of the square error (ISE) and the integral of the square error multiplied by time (ITSE). We showed that by using the fractional-order approach, we can reduce the values on the ISE and ITSE indices; hence, we guaranteed a full synchronization between the master and slave system. Our analysis shows that when using fractional derivatives with variable order, the ISE and ITSE indices have a lower value than when using the classical derivatives. We used the definition of Atangana-Baleanu-Caputo and Liouville-Caputo derivatives for the three examples mentioned in this work. We numerically solved the equations using the Adams method. Our results show that when using the fractional-order approach, the ISE and ITSE indices are lower than the integer-order case.
引用
收藏
页码:7987 / 8003
页数:17
相关论文
共 55 条
[1]   NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model [J].
Atangana, Abdon ;
Baleanu, Dumitru .
THERMAL SCIENCE, 2016, 20 (02) :763-769
[2]   Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators [J].
Azar, Ahmad Taher ;
Adele, Ngo Mouelas ;
Alain, Kammogne Soup Tewa ;
Kengne, Romanic ;
Bertrand, Fotsin Hilaire .
COMPLEXITY, 2018,
[3]  
Baleanu D., 2011, Fractional Dynamics and Control
[4]   Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus [J].
Baleanu, Dumitru ;
Ghanbari, Behzad ;
Asad, Jihad H. ;
Jajarmi, Amin ;
Pirouz, Hassan Mohammadi .
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2020, 124 (03) :953-968
[5]   The fractional features of a harmonic oscillator with position-dependent mass [J].
Baleanu, Dumitru ;
Jajarmi, Amin ;
Sajjadi, Samaneh Sadat ;
Asad, Jihad H. .
COMMUNICATIONS IN THEORETICAL PHYSICS, 2020, 72 (05)
[6]  
Cao JY, 2005, PROCEEDINGS OF 2005 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-9, P5686
[7]   The stability of chaos synchronization of the Japanese attractors and its application [J].
Chen, HK ;
Lin, TN ;
Chen, JH .
JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS BRIEF COMMUNICATIONS & REVIEW PAPERS, 2003, 42 (12) :7603-7610
[8]   Parameters identification and synchronization of chaotic systems based upon adaptive control [J].
Chen, Shihua ;
Lü, Jinhu .
Physics Letters, Section A: General, Atomic and Solid State Physics, 2002, 299 (04) :353-358
[9]   On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning [J].
Coronel-Escamilla, A. ;
Torres, F. ;
Gomez-Aguilar, J. F. ;
Escobar-Jimenez, R. F. ;
Guerrero-Ramirez, G. V. .
MULTIBODY SYSTEM DYNAMICS, 2018, 43 (03) :257-277
[10]   Design of a state observer to approximate signals by using the concept of fractional variable-order derivative [J].
Coronel-Escamilla, A. ;
Gomez-Aguilar, J. F. ;
Torres, L. ;
Valtierra-Rodriguez, M. ;
Escobar-Jimenez, R. F. .
DIGITAL SIGNAL PROCESSING, 2017, 69 :127-139