小世界网络同步的非线性时滞反馈控制

The Nonlinear Delayed Feedback Control of the Small-World Network

大脑的病态同步放电活动会导致一些神经类疾病,如帕金森、癫痫等.采用Izhikevich神经元模型构建一个兴奋-抑制小世界网络,增加网络的耦合强度能够实现网络的同步簇放电.对网络施加非线性时滞反馈控制,网络的这种同步活动很快消失.仿真结果表明:微分形式的反馈控制去同步的同时,保持了单个神经元的固有放电特性,且这种反馈控制不具有侵害性.直接形式的反馈控制通过抑制神经元的放电活动来抑制网络的同步,这种形式的反馈控制对刺激参数的变化具有鲁棒性,更适用于实际的深度脑刺激术.

Pathological synchronous discharge of brain can cause several neurological diseases such as Parkinson’s diseases and epilepsy. To tackle this problem,a small-world network is constructed based on the Izhikevichneuron model,which consist of excitatory neurons and inhibitory neurons,and increasing the coupling strength can realize the bursting phase synchronization of the network. When the nonlinear delayed feedback control is applied to the network,the synchronization activity of the network quickly disappears. Simulation results show that the differential feedback control does not destroy discharge characteristics of the individual unit,but only by changing the correlation of neuron discharge to eliminate synchronization. However,the direct feedback control suppresses the synchronization of the network by inhibiting the firing activity of neurons,which is robust against the variations of stimulation parameters and it is more suitable clinical need for mild stimulation techniques.