Abstract
Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods.
Highlights
Neural networks have been put more and more attention up to now [1,2,3,4]
Taking into consideration these facts, it is easy to know that combining an infinite memory term into the model of neural network is a big development, and it is advisable to research fractional-order neural networks (FONNs)
Let us discuss the synchronization of FONN by utilizing linear control
Summary
Neural networks have been put more and more attention up to now [1,2,3,4]. Ranging from combinatorial optimization, pattern recognition, associative memories and many other fields, neural networks have been successfully used. The uniform stability of fractional-order neural networks (FONNs) with delay is studied in [10]. Literature [11] discusses the synchronization problem for the uncertain fractional-order chaotic systems by means of adaptive fuzzy control. The problem of stability analysis of fractional-order complex-valued Hopfield neural networks with time delays are considered in [27]. As discussed in [21,28], how to analyze the stability of fractional-order nonlinear systems is still not well investigated and requires further study. There are some stability theories about the traditional neural networks Most of these results are driven by choosing appropriate Lyapunov functions, but these methods can’t be extended into FONN directly.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
