Koinfo Jean Baptiste, Sriram Sridevi, Jacques Kengne, Karthikeyan Anitha
Faculty of Sciences, University of Dschang, Dschang, Cameroon.
Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India.
Cogn Neurodyn. 2024 Dec;18(6):3873-3899. doi: 10.1007/s11571-024-10170-5. Epub 2024 Sep 6.
The studies conducted in this contribution are based on the analysis of the dynamics of a homogeneous network of five inertial neurons of the Hopfield type to which a unidirectional ring coupling topology is applied. The coupling is achieved by perturbing the next neuron's amplitude with a signal proportional to the previous one. The system consists of ten coupled ODEs, and the investigations carried out have allowed us to highlight several unusual and rarely related dynamics, hence the importance of emphasizing them. The main analysis tools that have helped in obtaining the results presented are phase portraits, bifurcation diagrams, and the Maximal Lyapunov exponent. In this system, we have observed phenomena such as the coexistence of homogeneous and heterogeneous attractors, period-doubling crisis, parallel branches, and the path leading to hyperchaotic multi-spiral. All attractors are non-hidden as they originate from well-known equilibrium points. The system has 254 equilibrium points, among which only 32 undergo a Hopf bifurcation followed by period-doubling, leading to a merging crisis phenomenon until the final hyperchaotic multi-spiral attractor. For the same parameter values (coupling or dissipation), a maximum of 30 attractors for the coupling coefficient and 32 attractors for dissipation coexist, and illustrated by the phase portraits. Virtual verification using Pspice and practical verification using an Arduino Mega 2580 microcontroller of the model have also been reported. They are in perfect agreement with the behaviors resulting from numerical investigations. The circuit energy and dimensionless energy has been estimated and the scale relation established. The results presented further enrich previous and recent work in the study of the nonlinear dynamics of Hopfield-type neural networks. Additionally, it is important to mention that cyclic coupling typology may be used as an alternative approach in generating multi-spiral signals in Hopfield oscillators.
本论文中的研究基于对一个由五个霍普菲尔德型惯性神经元组成的均匀网络的动力学分析，该网络应用了单向环耦合拓扑结构。耦合是通过用与前一个神经元信号成比例的信号扰动下一个神经元的幅度来实现的。该系统由十个耦合的常微分方程组成，所进行的研究使我们能够突出几种不寻常且很少相关的动力学，因此强调它们很重要。有助于获得所呈现结果的主要分析工具是相图、分岔图和最大李雅普诺夫指数。在这个系统中，我们观察到了诸如均匀吸引子和异质吸引子共存、倍周期危机、平行分支以及通向超混沌多螺旋的路径等现象。所有吸引子都不是隐藏的，因为它们源自众所周知的平衡点。该系统有254个平衡点，其中只有32个经历霍普夫分岔，随后是倍周期分岔，导致合并危机现象，直到最终的超混沌多螺旋吸引子。对于相同的参数值（耦合或耗散），耦合系数最多有30个吸引子，耗散最多有32个吸引子共存，并由相图说明。还报告了使用Pspice进行的虚拟验证以及使用Arduino Mega 2580微控制器对该模型进行的实际验证。它们与数值研究得出的行为完全一致。已经估计了电路能量和无量纲能量，并建立了比例关系。所呈现的结果进一步丰富了先前和近期关于霍普菲尔德型神经网络非线性动力学研究的工作。此外，重要的是要提到，循环耦合类型可以用作在霍普菲尔德振荡器中生成多螺旋信号的替代方法。
