神经元放电模型:从微分方程到非线性映象

Neural discharge patterns:from differential equations to nonlinear mappings

目的概括和总结现有的神经元模型,并对典型的连续模型和离散模型的放电特征及其动力学机制进行分析比较。方法构建含有一个快变量和一个慢变量的二维映象,用一个简单的映象模型来替代复杂的微分方程形式能使模型简化。结果调节映象中的参数能观察到与实际相符的各种不同的放电模式,通过映象的耦合也能观察到同步现象。结论简单的映象模型能替代原来的微分方程形式模拟神经元放电。

Aim To generalize and summarize existing neuron models as well as analyse and compare the discharge characteristics and dynamic mechanisms of typical continuous and discrete models. Methods A two-dimensional mappings containing one fast and one slow variable has been built,and neural model has been simplified by replacing complicated differential equations with a simple mapping. Results The various discharge patterns can be observed through adjusting parameters of the mappings.Coupling of mappings appear synchronization. Conclusion The simple mappings could replace the differential equations and simulate the neural discharge.