Reinker Stefan, Puil Ernest, Miura Robert M
Department of Mathematics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada BC V6T 1Z2.
Bull Math Biol. 2003 Jul;65(4):641-63. doi: 10.1016/S0092-8240(03)00026-0.
Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.
当用不同频率的小正弦波信号刺激时，丘脑神经元表现出阈下共振；当给这些信号添加噪声时，丘脑神经元表现出随机共振。我们使用蒙特卡罗模拟研究一个随机的Hindmarsh-Rose模型，以研究噪声与阈下共振如何共同导致放电模式中的偏好频率。由此产生的随机共振（SR）表现出一个偏好的放电频率，该频率对噪声幅度的依赖性近似呈指数关系。在类似的实验中，在噪声下检测α函数输入的可靠性方面发现了频率依赖性随机共振，α函数输入对神经元来说是更现实的输入。对方程的数学分析表明，频率偏好源于慢变量的动力学。由于快速子系统接近霍普夫分岔点，噪声随后可以将共振转移到放电阈值之上。我们的结果可能对网络中丘脑神经元的行为有影响，噪声可使膜电位在不同的共振模式之间切换。
