Nonlinear feedback synchronization of hyperchaos in higher dimensional systems

Nonlinear feedback synchronization of hyperchaos in higher dimensional systems 1 first-author 2 China Institute of Atomic Energy, Beijing 102413 China Institute of Atomic Energy, Beijing 102413 Department of Physics, The University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada Department of Physics, The University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada Nonlinear feedback functional method is presented to realize synchronization of hyperchaos in higher dimensional systems. New nonlinear feedback functions and superpositions of linear and nonlinear feedback functions are also introduced to synchronize hyperchaos. The robustness of the method based on the flexibility of choices of feedback functions is discussed. By coupling well-known chaotic or chaotic-hyperchaotic systems in low-dimensional systems, such as Lorenz system, Van der Pol oscillator, Duffing oscillator and Rössler system, ten dimensional hyperchaotic systems are formed as the model systems. It can be found that there is not any noticeable difference in synchronization based on the numbers of positive Lyapunov exponents and of dimensions. Hyperchaos Synchronization Nonlinear feedback functions Ten-dimension. References Kapitanial T , Chua L . Inter J Bifurcation and Chaos , 1994 ; 4 : 477 Inter J Bifurcation and Chaos Lai Y C , Grebogi C . Phys Rev , 1994 ; 50E : 1894 Phys Rev Fang Jin-Qing . Chinese Science Bulletin , 1995 : 40 : 988 Chinese Science Bulletin Fang Jin-Qing . Chi J Nucl Phys , 1996 ; 18 : 182 Chi J Nucl Phys Fang Jin-Qing . Chi J Nucl Phys , 1996 ; 18 : 244 Chi J Nucl Phys Fang Jin-Qing . Chi J Nucl Phys , 1997 ; 19 : 63 Chi J Nucl Phys Kocaver L , Parlitz U . Phys Rev Lett , 1995 ; 74 : 5028 Phys Rev Lett Shinbrot T . Advances in Physics , 1995 ; 44 : 173 Advances in Physics Fang Jin-Qing . Progress in Physics (in Chinese) , 1996 ; 16 : 1 Progress in Physics (in Chinese) Fang Jin-Qing . Progress in Physics (in Chinese) , 1996 ; 16 : 137 Progress in Physics (in Chinese) Pen J H , Ding E J , Ding M et al . Phys Rev Lett , 1996 ; 76 : 904 Phys Rev Lett Ali M K , Fang Jin-Qing . Phys Rev , 1997 ; 55E : 5285 Phys Rev Ali M K , Fang Jin-Qing . Discrete dynamics in nature and society , Phys Rev E , October, 1997 Discrete dynamics in nature and society Fang Jin-Qing , Ali M K . Nucl Sci Tech , 1997 ; 8 : 129 Nucl Sci Tech Crawford J Q . J Stat Phys , 1995 ; 74 : 4341 J Stat Phys Schuster H G , Niebur E , Hunt E R et al . Phys Rev Lett , 1996 ; 76 : 400 Phys Rev Lett Pecora L , Carrol T . Phys Rev Lett , 1990 ; 64 : 1196 Phys Rev Lett Carrol T , Pecora L . IEEE Trans Circuits and Systems , 1991 ; 38 : 453 IEEE Trans Circuits and Systems Guemez J , Matias M A . Phys Rev E , 1995 ; 52 : R2145 Phys Rev E Guemez J , Matias M A . Phys Rev E , 1996 ; 53 : 3059 Phys Rev E Wiesenfeld K , Colet Pere , Strogatz Steven H . Phys Rev Lett , 1996 ; 76 : 404 Phys Rev Lett Chua L O , Kocarev L , Eckert K et al . Inter J Bifurcation and Chaos , 1992 ; 2 : 705 Inter J Bifurcation and Chaos Pyragas K . Phys Lett A , 1992 : 170 : 421 Phys Lett A Chen G , Dong X . IEEE Trans Circuits and Systems , 1993 ; 40 : 591 IEEE Trans Circuits and Systems Dong X , Chen G . Proc of American Control Conf , Chicago, IL , June, 1992 ; 2234 Hu G , Qu Z L , He K . Inter J Bifurcation and Chaos , 1995 ; 5 : 901 Inter J Bifurcation and Chaos Qu Z L , Hu G . Phys Rev E , 1993 ; 49 : 1099 Phys Rev E Qu Z L , Hu G . Phys Lett A , 1993 ; 178 : 265 Phys Lett A Qu Z L , Hu G . Phys Rev Lett , 1994 ; 74 : 1736 Phys Rev Lett This work is supported by funding to Fang Jin-Qing from National Nuclear Industry Science Foundation of China, and China National Project of Science and Technology for Returned Students in Non-Education System as a key project; and also by NSERCC grant to M. K. Ali from the National Research Council of Canada. 1997-05-20 1997-11-01 2021-02-05 1997 Nuclear Science and Techniques 4 8