Cheng Minyuan, Wang Kaihua, Xu Xianying, Mou Jun
School of Information Science and Engineering, Dalian polytechnic University, Dalian, 116034 China.
Department of Basic Education, Liaoning Vocational College of Light Industry, Dalian, 116100 China.
Cogn Neurodyn. 2024 Dec;18(6):3963-3979. doi: 10.1007/s11571-024-10172-3. Epub 2024 Sep 13.
Two types of neuron models are constructed in this paper, namely the single discrete memristive synaptic neuron model and the dual discrete memristive synaptic neuron model. Firstly, it is proved that both models have only one unstable equilibrium point. Then, the influence of the coupling strength parameters and neural membrane amplification coefficient of the corresponding system of the two models on the rich dynamical behavior of the systems is analyzed. Research has shown that when the number of discrete local active memristor used as simulation synapses in the system increases from one to two, the coupling strength parameter of the same memristor has significantly different effects on the dynamical behavior of the system within the same range, that is, from a state with periodicity, chaos, and periodicity window to a state with only chaos. In addition, under the influence of coupling strength parameters and neural membrane amplification coefficients, the complexity of the system weakens to varying degrees. Moreover, under the effect of two memristors, the system exhibits a rare and interesting phenomenon where the coupling strength parameter and the neural membrane amplification coefficient can mutually serve as control parameter, resulting in the generation of a remerging Feigenbaum tree. Finally, the pseudo-randomness of the chaotic systems corresponding to the two models are detected by NIST SP800-22, and relevant simulation results are verified on the DSP hardware experimental platform. The discrete memristive synaptic neuron models established in this article provide assistance in studying the relevant working principles of real neurons.
本文构建了两种神经元模型，即单离散忆阻突触神经元模型和双离散忆阻突触神经元模型。首先，证明了这两种模型都只有一个不稳定平衡点。然后，分析了这两种模型相应系统的耦合强度参数和神经膜放大系数对系统丰富动力学行为的影响。研究表明，当系统中用作模拟突触的离散局部有源忆阻器数量从一个增加到两个时，同一忆阻器的耦合强度参数在相同范围内对系统动力学行为有显著不同的影响，即从具有周期性、混沌和周期性窗口的状态转变为仅具有混沌的状态。此外，在耦合强度参数和神经膜放大系数的影响下，系统的复杂性会有不同程度的减弱。而且，在两个忆阻器的作用下，系统呈现出一种罕见且有趣的现象，即耦合强度参数和神经膜放大系数可以相互作为控制参数，从而产生重新合并的费根鲍姆树。最后，利用NIST SP800 - 22对这两种模型对应的混沌系统的伪随机性进行了检测，并在DSP硬件实验平台上验证了相关仿真结果。本文建立的离散忆阻突触神经元模型为研究真实神经元的相关工作原理提供了帮助。
