Abstract
This research is chiefly concerned with the stability and Hopf bifurcation for newly established fractional-order neural networks involving different types of delays. By means of an appropriate variable substitution, equivalent fractional-order neural network systems involving one delay are built. By discussing the distribution of roots of the characteristic equation of the established fractional-order neural network systems and selecting the delay as bifurcation parameter, a novel delay-independent bifurcation condition is derived. The investigation verifies that the delay is a significant parameter which has an important influence on stability nature and Hopf bifurcation behavior of neural network systems. The computer simulation plots and bifurcation graphs effectively illustrate the reasonableness of the theoretical fruits.
Highlights
It is widely known that neural network systems own great application value in plenty of areas such as disease treatment, pattern recognition, intelligent control, biology, information processing, control technique, and so on [1,2,3,4,5,6]
Time delay usually occurs in lots of neural networks and biological systems since there is delay of information transmission of distinct neurons and the response of diverse biotic populations. erefore, grasping the effect of delay on the dynamic law for many dynamical models is a key topic in contemporary science
Xu et al [20] made a detailed analysis on the stability and the onset of Hopf bifurcation for fractional-order BAM neural networks involving time delays
Summary
It is widely known that neural network systems own great application value in plenty of areas such as disease treatment, pattern recognition, intelligent control, biology, information processing, control technique, and so on [1,2,3,4,5,6]. Fractional-order differential dynamical system has aroused widespread interest from many scholars since it owns great application prospect in a lot of fields such as control technique, various physical waves, neural network models, biological systems, and so on [14, 15]. Some researchers pay much attention to Hopf bifurcation of fractional-order delayed neural networks and some good results have been achieved. Xu et al [20] made a detailed analysis on the stability and the onset of Hopf bifurcation for fractional-order BAM neural networks involving time delays. Xu et al [23] dealt with Hopf bifurcation of fractional-order BAM neural network models involving multiple delays. Motivated by the discussion above, our concern is the stability and Hopf bifurcation for fractional-order neural networks involving discrete delays and distributed delays.
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