Hybrid synchronization and parameter identification of uncertain interacted networks

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

“…Remark (i) The topological structures of two networks shown quantitatively by the connections $$$ {x}_{ij}(k) $$$ and $$$ {\overline{x}}_{ij}(k) $$$ can be different, and the dynamics of the isolated nodes of two networks can be different, which are both required to be the same in References 31‐35; and compared with References 32‐35, the linear parts are not required to be shown in the above models () and (). (ii) In the models () and (), the interactions between $$$ S $$$ and $$$ \overline{S} $$$ are considered by employing the unknown coupling vector functions $$$ {h}_i\left[z(k),\overline{z}(k),k\right] $$$ and $$$ {\overline{h}}_i\left[z(k),\overline{z}(k),k\right] $$$, respectively, by which the dynamic models of networks are mathematically proposed more general than the ones of existing literature, the models of interactive networks in References 29, 31, 36‐39 can be regarded as the special ones of the models () and (). (iii) The utility of the two interactive networks models () and (), for example, can be explained by the clustering for a CDN with $$$ 2N $$$ nodes, and the dynamics of the CDN can be expressed by the equation …”

“…Compared with the inner synchronization, the outer synchronization is still regarded as the dynamic behavior of nodes, but the nodes belong to different networks. In recent years, the researches on outer synchronization have attracted much attention to investigate the structure and function of networks via the synthesized control schemes 2,5,7,12,16‐18,29,31‐39 …”

“…In recent years, the researches on outer synchronization have attracted much attention to investigate the structure and function of networks via the synthesized control schemes. 2,5,7,12,[16][17][18]29,[31][32][33][34][35][36][37][38][39] However, it should be noted that most of the existing results have been concerned with the outer synchronization for continuous-time CDNs instead of the discrete-time CDNs. With the development of computer science, the discrete-time characteristics of signal transmission are highlighted due to the pulse technology, microprocessor and digital components, a large number of real networks in biology, ecology, 40 aerospace, 41 and economy 42 show the discrete-time characteristics and need to be described mathematically by discrete-time models.…”

Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

“…Recently, significant effort has been devoted to the study of the synchronization of complex dynamical networks [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. However, the synchronization criteria in most of the existing studies contain unknown parameters, thereby making system synchronization difficult for workers to verify.…”

“…Consequently, synchronization, which is a typical collective behavior of complex dynamical networks, has become active popular research topic. Synchronization in dynamical networks has been extensively investigated by researchers from various fields [5][6][7][8][9][10][11][12][13].…”