General decay anti-synchronization and H∞ anti-synchronization of coupled reaction-diffusion complex-valued memristive neural networks

This paper studies the general decay anti-synchronization (GDAS) and general decay H∞ anti-synchronization (GDHAS) problems for coupled reaction–diffusion complex-valued memristive neural networks (CRDCVMNNs) without and with time delays. First of all, the concept of GDHAS under the complex-valued case is firstly presented based on the definitions of ψ-type function and ψ-type stability. According to this concept, we further prove a novel lemma which will be used throughout this paper under a new assumption. This lemma is very crucial which gives a new sufficient condition for achieving GDAS of CNNs in complex field. Then, by using the derived lemma and designing a suitable nonlinear feedback controller, some criteria for CRDCVMNNs without and with time delays to realize GDAS and GDHAS are established. At last, two numerical examples are used to verify the effectiveness of the anti-synchronization results.