Pinning synchronization of fractional‐order complex networks with adaptive coupling weights

Abstract

This work studies the issue of synchronization control for a type of fractional-order complex networks, in which the adaptive coupling matrix is considered under the directed topology structure. A pinning control strategy, with the free selection of pinning nodes, is adopted for the synchronization goal. Then, by absorbing the information of eigenvectors and adaptive laws for the coupling matrix, a new Lyapunov function is constructed, by which, and with the assistance of Gronwall inequality and network features, the sufficient condition for Mittag-Leffler synchronization of the fractional-order network is established. Accordingly, an easy verifiable algebraic criterion is further derived by means of some matrix inequalities. Besides, we also discuss the effect of outer coupling strength on the achievement of network synchronization. Finally, a numerical experiment is performed to show the evidence of the correctness and effectiveness of the proposed results.

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

“…, 𝜔 = 2q max 1≤i≤N {𝛾 i }, then the controlled error Lur'e networks ( 6) is exponentially stable. To be more specific, the global and exponential synchronization between the coupled Lur'e networks (1) and the leader Lur'e system (2) could be eventually achieved under the proposed impulsive adaptive feedback controller (4) and the designed adaptive updating law (5). In addition, the convergence velocity is estimated as 𝛿 2 , where 𝛿 is a unique solution of the parameter function 𝛿 + ( ln 𝜌…”

“…Researches on the dynamical behaviors of complex networks, such as spreading dynamics, cascade reaction, human opinion dynamics and network synchronization, have been conducted for couple years. [1][2][3][4][5] As a representative collective dynamical behavior, synchronization has received extensive attention from scientists in multiple fields due to its widespread existence in natural as well as artificial systems and largely untapped potential of applications. Currently, synchronization theory has been implemented in various application scenarios such as transportation planning, secure communication and image encryption.…”

“…Generally, complex networks can be regarded as complicated coupling structures constructed by multiple dynamical systems. Researches on the dynamical behaviors of complex networks, such as spreading dynamics, cascade reaction, human opinion dynamics and network synchronization, have been conducted for couple years 1‐5 . As a representative collective dynamical behavior, synchronization has received extensive attention from scientists in multiple fields due to its widespread existence in natural as well as artificial systems and largely untapped potential of applications.…”

Quasi-synchronization of fractional-order complex networks with random coupling via quantized control

“…In many studies, researchers have focused on setting the controller to make the error of the complex network system approach zero with the advancement of time. [11][12][13][14] However, because of the existence of system disturbance in practical applications and because this disturbance is difficult to eliminate completely, sometimes the synchronization error cannot fully converge to zero. [15] Therefore, based on the above considerations, it is particularly necessary to study how to control the upper limit of the synchronization error by setting a controller to achieve quasisynchronization.…”

Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights

“…A number of important works discuss the synchronization of complex networks [14][15][16][17][18]. This literature shows node dynamics depending only on time.…”