%0 Journal Article %1 noauthororeditor %A Vaidyanathan, Sundarapandian %D 2011 %J International Journal of Advanced Information Technology (IJAIT) %K Adaptive Chaos Control Hybrid Liu Lü Synchronization System %N 6 %P 13-32 %R 10.5121/ijait.2011.1602 %T HYBRID SYNCHRONIZATION OF LIU AND LÜ CHAOTIC SYSTEMS VIA ADAPTIVE CONTROL %U http://airccse.org/journal/IJAIT/papers/1211ijait02.pdf %V 1 %X This paper derives new results for the hybrid synchronization of identical Liu systems, identical Lü systems, and non-identical Liu and Lü systems via adaptive control method. Liu system (Liu et al. 2004) and Lü system (Lü and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems addressed in this paper is achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Adaptive control method is deployed in this paper for the general case when the system parameters are unknown. Sufficient conditions for hybrid synchronization of identical Liu systems, identical Lü systems and non-identical Liu and Lü systems are derived via adaptive control theory and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the adaptive control method is very effective and convenient for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes.

@article{noauthororeditor, abstract = {This paper derives new results for the hybrid synchronization of identical Liu systems, identical Lü systems, and non-identical Liu and Lü systems via adaptive control method. Liu system (Liu et al. 2004) and Lü system (Lü and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems addressed in this paper is achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Adaptive control method is deployed in this paper for the general case when the system parameters are unknown. Sufficient conditions for hybrid synchronization of identical Liu systems, identical Lü systems and non-identical Liu and Lü systems are derived via adaptive control theory and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the adaptive control method is very effective and convenient for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes. }, added-at = {2019-09-09T08:46:53.000+0200}, author = {Vaidyanathan, Sundarapandian}, biburl = {https://www.bibsonomy.org/bibtex/2f1a50fdba22d23e72d72a46a164f76e4/ijaitislive}, doi = {10.5121/ijait.2011.1602}, interhash = {067d9e4712f06525c3ca54c3b5a0c889}, intrahash = {f1a50fdba22d23e72d72a46a164f76e4}, issn = {2231 - 1548 [Online] ; 2231 - 1920 [Print]}, journal = {International Journal of Advanced Information Technology (IJAIT)}, keywords = {Adaptive Chaos Control Hybrid Liu Lü Synchronization System}, language = {English}, month = {December}, number = 6, pages = {13-32}, timestamp = {2019-09-09T08:46:53.000+0200}, title = {HYBRID SYNCHRONIZATION OF LIU AND LÜ CHAOTIC SYSTEMS VIA ADAPTIVE CONTROL}, url = {http://airccse.org/journal/IJAIT/papers/1211ijait02.pdf}, volume = 1, year = 2011 }