Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion

• There is consider the reaction-diffusion term in fractional heterogeneous systems. Compared with the existing ordinary differential network models, the state variables in the HFCNNs we consider are based on space-time, which is more practical and generalized. • Different from the previous homogeneous network model, the heterogeneous coupled neural networks is studied. The previous processing method is no longer applicable. Based on the correlation of neighbor nodes, a novel distributed fractional-order adaptive control is proposed to realize Mittag-Leffler converge of synchronization errors into a small bounded set. • For with or without reference nodes, the quasi-synchronization and leader-following quasi-synchronization are achieved respectively. The time-varying of coupling strength can be designed appropriately so that under the adaptive controller, the convergence synchronization error can be sufficiently small, the convergence speed can be obtained. In this paper, the quasi-synchronization problem of heterogeneous fractional-order coupled neural networks (HFCNNs) is studied. In addition, we also take the spatial diffusion effect into consideration, and design an adaptive controller to attenuate the interference of heterogeneous terms. On the one hand, for quasi-synchronization, we propose a nonlinear distributed control law based on local information exchange between neighboring nodes, so that the synchronization error converges to a regulable bounded domain with a certain decay rate. On the other hand, leader-following quasi-synchronization, the reference trajectory is designed in advance and the corresponding distributed controller is developed to make the synchronization errors still tending to the bounded set. Finally, the simulation results show that the theoretical results are correct.