Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Abstract

Synaptic crosstalk is a prevalent phenomenon among neuronal synapses, playing a crucial role in the transmission of neural signals. Therefore, considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks is highly necessary. In this paper, we propose a heterogeneous discrete neural network (HDNN) consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron. These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered. The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents. It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths. Furthermore, the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated, revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

Dynamic Analysis and Field-Programmable Gate Array Implementation of a 5D Fractional-Order Memristive Hyperchaotic System with Multiple Coexisting Attractors

“…The parameters are as follows: b = 2, c = 7, d = 4, k = 5, m = 0.1, n = 0.01. The fractional-order system, denoted as (19), is characterized by an order of e = 0.7, with 20,000 iterations and a step size of 0.005, operating within the parameter range of [10,14]. The Lyapunov exponent spectrum, depicted in Figure 6a, shows that when a varies within the interval [10,11], the three lines consistently remain close to or below zero, indicating no positive Lyapunov exponents and positioning the system (19) in a periodic state.…”

“…Nonlinear science is theoretically significant and promising for practical applications across various life aspects. Over the past decade, researchers have extensively applied it in fields such as image encryption [1][2][3][4][5], electronic circuits [6][7][8][9][10], chaos synchronization [11][12][13][14][15], pseudo-random number generators [16][17][18][19][20], and neural networks [21][22][23][24][25], among others. The complex structure of chaotic attractors enhances their dynamic properties.…”

Coexisting discharge and synchronization of heterogeneous discrete neural network with crosstalk memristor synapses

“…复杂、非易失存储及类神经突触可塑性等独特性质。因而，忆阻器是模拟生物神经突触的理 想器件 [21][22][23][24] ，为人工神经网络的构建提供了新的思路。局部有源性被认为是动力系统复杂性 的起源 [25] 。局部有源忆阻器能放大无限小能量振荡行为，应用于神经网络系统或神经元电 路时易于诱发各类神经形态放电行为 [26] 。因此，利用局部有源忆阻器模拟生物神经突触受 到越来越多的关注。将离散局部有源忆阻器引入人工神经网络或神经元，可以更准确地模拟 生物神经元之间的电活动和信息传递，有助于揭示神经系统疾病的电生理学机制。文献 [27] 基于无离散忆阻器、离散忆阻器模拟电磁辐射刺激、离散局部有源忆阻器模拟生物突触等方 式构建了三种离散神经网络模型；研究表明，离散忆阻器可使得神经网络模型产生更为复杂 的混沌放电动力学行为。文献 [28]构建了一类离散忆阻 Rulkov 神经元模型，研究发现忆阻 器可以有效地模拟离散神经元模型的磁感应效应。此外，文献 [29]研究了基于离散忆阻器的 分数阶神经网络，发现其具有比整数阶神经网络更丰富的动力学行为。事实上，生物神经信 息的处理和传递由不同脑区神经元的电磁活动共同完成，因此，探索异质离散神经网络的放 电动力学和同步行为具有重要实际意义 [13] 。 突触间的串扰由神经递质从一个突触溢出至另一个突触引起。 突触神经递质的溢出将对 相邻突触的连接强度产生干扰，因此，突触串扰将影响神经信号的放电及传输特性 [30,31] 。文 献 [32]提出一种基于忆阻器突触的联想记忆电路，并研究了突触串扰对忆阻器功能的影响。 文献 [33]揭示了不同串扰强度下，忆阻器耦合 HR 神经网络平衡点的数量和稳定性具有多样 性。另外，越来越多的证据表明，突触串扰存在于多个不同大脑区域。例如，文献 [34]建立 了一个异质神经网络，探讨了串扰强度对神经网络放电活动的影响，发现随着串扰强度的降 低，异质神经元的放电行为从初始振荡逐渐过渡到完全同步。文献 [35]则从数值模拟角度探 讨了串扰强度对异质离散神经网络放电行为和同步行为的影响。然而，目前尚没有关于突触 串扰强度对神经网络共存放电行为影响的研究。事实上，共存放电意味着神经系统的不同等 待状态 [36]…”