Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Abstract

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.

Price Dynamics of a Delay Differential Cobweb Model

“…Tus, the smaller the fractional-order, the more drastic the instability of the function becomes. Tis assertion will be further investigated in comparison with other models [17] in future research, where the bifurcation properties of the fractional-order delay diferential cobweb model will be discussed as shown in the related articles [17][18][19][20][21] and then assessed for the practical implication of the bifurcation of price in the market.…”

Bifurcation insight for a fractional‐order stage‐structured predator–prey system incorporating mixed time delays

“…Naturally, the impact of time delay on Hopf bifurcation has attracted great attention from numerous scholars. In recent years, the study on Hopf bifurcation for integer-order dynamical models is relatively mature, but the investigation on Hopf bifurcation for fractional-order dynamical models is very rare (see previous studies [26][27][28][29][30][31][32] ). In particular, the study on Hopf bifurcation of prey-predator models is even less (see previous works 33,34 ).…”

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

“…Importantly, in the implementation process of NNs, the transmission speed of the hardware devices used in the design is limited, and there may be delays encountered. Delay may have significant impacts on NNs, leading to unexpected complex dynamics [23][24][25][26][27][28][29][30][31][32][33][34]. For example, Zhou et al [24] deal with the global exponential stability for the MCGNN, and got several stability conditions.…”