Huang Chengdai, Mo Shansong, Cao Jinde
School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000 China.
School of Mathematics, Southeast University, Nanjing, 210096 China.
Cogn Neurodyn. 2024 Jun;18(3):1379-1396. doi: 10.1007/s11571-023-09934-2. Epub 2023 Feb 28.
The dynamics of integer-order Cohen-Grossberg neural networks with time delays has lately drawn tremendous attention. It reveals that fractional calculus plays a crucial role on influencing the dynamical behaviors of neural networks (NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge (reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter (longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfully keeping away from the intricate classified discussions. Eventually, the developed analytic results are nicely showcased by the simulation examples.
具有时滞的整数阶Cohen-Grossberg神经网络的动力学近来引起了极大关注。研究表明,分数阶微积分在影响神经网络(NNs)的动力学行为方面起着关键作用。本文研究了具有两种不同泄漏延迟和通信延迟的分数阶Cohen-Grossberg神经网络(FOCGNNs)的稳定性和分岔问题。首先得到了关于泄漏延迟的分岔结果。然后,将通信延迟视为分岔参数,以检测所研究的FOCGNN的分岔临界值,并得到通信延迟引起的分岔条件。我们进一步发现,分数阶可以扩大(缩小)所研究的FOCGNN的稳定区域。此外,我们发现,对于相同的系统参数,分数阶神经网络(FONN)到平衡点的收敛时间比整数阶神经网络的收敛时间短(长)。在本文中,与先前的机制相比,处理具有三重超越项的延迟FOCGNNs特征方程的现有方法简洁、新颖且灵活,这是由于巧妙地避免了复杂的分类讨论。最后,通过仿真例子很好地展示了所得到的解析结果。