Abstract
The finite-time lag synchronization problem of memristive neural networks with multi-links (MNNLs) is discussed with the adaptive controllers, and the discrete and distributed time-varying delays are included in the network models. With the Lyapunov functional method and the properties of inequality, two different finite-time methods are adopted to prove and compare the effects of the two proposed theorems, and three corollaries are obtained and to be analyzed. Using the assumptions of Lipschitz continuous and boundedness of the activation functions, three lemmas are derived to deal with the difficulty caused by the memristive jumping properties and synchronization lag feature, which make the proof of the theorems simple and clear. Based on that whether time-varying delays are included, with the adaptive control strategy, we design delay-independent and delay-dependent adaptive controllers with different adaptive parameters for the MNNLs respectively. Finally, two numerical simulations are given to show the effectiveness and correctness of the obtained theoretical results.
Highlights
The memristor is considered as the fundamental electronic component following with resistors, capacitors and inductors, and Fig. 1 shows the mutual relationships of the four electronic components [1]
MAIN RESULTS In this part, the adaptive lag synchronization problem is investigated with the finite-time methods and Lyapunov stability theory, and two theorems with different finite-time lag synchronization and different adaptive controllers are proposed
DELAY-DEPENDENT ADAPTIVE CONTROLLER In this subsection, we research on the finite-time lag synchronization of the MNNLs with mixed time-varying delays via the adaptive controller with time-varying delays
Summary
The memristor is considered as the fundamental electronic component following with resistors, capacitors and inductors, and Fig. 1 shows the mutual relationships of the four electronic components [1]. The memristor represents the relation between magnetic flux and electric charge, and the memristance changes with the amount of the passed electric charge, this reflects the memory characteristic. These features of memristors are very close to the characteristics of neuronal synapses, so the memristor is considered to be very suitable for constructing synapses of artificial neural networks [3]–[6]. Memristive neural networks (MNNs) have quickly become a research hotspot in recent years.
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