Finite-time Synchronization Of General Chaotic Systems With Different Dimensions And Complex Networks

Synchronization of two systems means that they start from different initial conditions, and with time going by, their trajectories gradually come to a consistent state. In recent years, the asymptotic synchronization in most literature discussed that when the time converges to infinity, the chaotic systems can obtain synchronous state or not. Nevertheless, as a matter of fact, this requirement sometimes is not realistic.For instance, in secure communication, provided that chaotic oscillators could not achieve synchronization within finite time, or enciphered message could not be recovered or forwarded successfully within finite time, then irretrievable loss would be caused on both occasions.Based on what mentioned above, in this paper, the finite-time synchronization of two general chaotic systems and complex networks are investigated. The main research content and innovation are the following two aspects:(1) In point of the existing literature, the synchronization of chaotic systems preliminarily concentrated upon the chaotic systems with same dimension and structure or with same dimension yet different structures. However, the theoretical research results for the finite-time synchronization of chaotic systems with different dimensions still have been relatively less so far.In this paper, three schemes of finite-time generalized synchronization of general drive systems and response systems with different dimensions are put forward in theory. At the same time, the magnitude relations of synchronization time and its theoretical proof in the first scheme and the second scheme are proposed. At last,Based on a three-dimensional Chen system and a two-dimensional Vander Pol system,a numerical modeling example is given to demonstrate the validity of proposed schemes and the correctness of theoretical results.(2) At present, a majority of the existing literature discussing the synchronization of complex networks chiefly assumed all the nodes are identical. And nearly all the literature did not allow for the finite-time synchronization of complex networks whose nodes have different structures. Obviously, in our real life, it is more realistic and more significant when considering the finite-time synchronization of this kind of complex networks.In this paper, the finite-time synchronous problems of complex networks the nodes of which have different structures are studied. Based upon Jensen inequality,finite-time Lyapunov stability theorem, and matrix theory, etc., a type of complex networks is constructed that have different nodes. A scheme of the finite-time synchronization with regard to this complex networks is achieved. The undetermined coupled function is obtained as well. Finally, Qi system, Lü system, and R?ssler system being taken as the nodes of the complex networks, a numerical simulation is presented to verify the effectiveness of the proposed schemes and the correctness of theoretical results.