二维格子神经元网络的振动共振和非线性振动共振∗

摘要

Response characteristics of FitzHugh-Nagumo neurons to low frequency signal have been investigated by numerical simulation. Neurons are arranged on a square-lattice and are subjected to two frequency signals. Results show that, vibrational resonance of the membrane potential can be induced by varying the amplitude of the high-frequency signal, when the control parameter is selected in the excitable region. In addition, the responses of neurons to higher harmonics of low-frequency signal have been studied, and nonlinear vibrational resonances are also found. With the increase of frequency in the low-frequency signal, the response of the system to low-frequency signal can resonate. Thus, the double resonance can occur by changing the frequency in low-frequency signal and the amplitude in high-frequency signal. Moreover, effects of electrical synapses and chemical synapses on vibrational resonance and nonlinear vibrational resonance of the neurons have also been studied. Effect of the number of neurons, which are subjected to two frequency signals in the square-lattice, on the response characteristic of the system is also studied. It is found that the response characteristic of the electrical coupling neurons is quite different from that of chemical coupling neurons.%本文采用数值模拟的方法，在通过电突触耦合或化学突触耦合的二维格子神经元网络中，研究了FitzHugh-Nagumo神经元受到双频信号输入时神经元网络对低频信号的响应特性。结果表明：当固定受到双频输入信号的神经元在体系中所占的比例且FitzHugh-Nagumo神经元参数处于可激发区域时双频信号中的高频部分可诱导出动作电位产生，而且随着高频输入信号强度的增加，神经元网络对低频输入信号响应先增大后减小，出现了极大值，即发生了振动共振现象。另外本文还研究了神经元网络对低频输入信号的二次谐波的响应，同样发现了非线性振动共振现象，并且体系对低频信号的响应随着其频率ω的增加也产生共振现象，即发生了双共振现象。上述共振现象在以电突触耦合的二维格子神经元网络中和以化学突触耦合的二维格子神经元网络中都可以观察到。当固定双频输入信号中高频输入信号强度时，随着受到双频输入信号的神经元在体系中所占比例的变化，电突触耦合的二维格子神经元网络对低频输入信号的响应与化学突触耦合的二维格子神经元网络对低频输入信号的响应相比有很大的不同。