Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Effects of double delays on bifurcation for a fractional-order neural network

Neural network bifurcation is an important nonlinear dynamic behavior of neural network, which plays an important role in cognitive calculation. The effects of leakage delay or communication delay on the stability and bifurcation of a fractional-order neural network (FONN) are researched. By viewing leakage delay or communication delay as the bifurcation parameters to detect the bifurcations conditions of the developed FONN, respectively, we capture the bifurcation points with regard to leakage delay or communication delay. It alleges that FONN exhibits excellent stability performance with choosing smaller values of them, and Hopf bifurcations emerge of FONN and induce poor performance if selecting a larger ones. In the end, numerical examples are employed to evaluate the feasibleness of the analytical discoveries.

Bifurcations due to different delays of high-order fractional neural networks

This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments.

Bifurcations in a fractional-order BAM neural network with four different delays

This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.