We investigate the generalized projective synchronization (GPS) problem of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with magneto-acoustical stimulation input. The improved neuronal model has advantages in depicting the biological characteristics of neurons and therefore exhibits complex firing behaviors. In addition, we consider the nonlinearity and uncertain parameters of the neuronal model as well as the unknown external disturbances, which make the synchronization control of the master-slave neuron system more difficult. For the synchronous firing rhythms of neurons, a neural network (NN) sliding mode algorithm for the FOEHR neuron system is derived by the Lyapunov approach. We use a radial basis NN to approximate the unknown nonlinear dynamics of the error system, and the adaptive parameters are robust to the approximation errors, model uncertainties and unknown external disturbances. Under the proposed control scheme, the master and slave neuron systems can achieve GPS in a finite amount of time and realize resilience for the uncertain parameters and the external disturbances. The simulation results demonstrate that the membrane potentials of the slave neuron synchronize with those of the master neuron in proportion and that the underlying synchronization errors converge towards an arbitrarily small neighborhood of zero.

我们调查具有磁声刺激输入的分数阶扩展Hindmarsh-Rose（FOEHR）神经元模型的广义投影同步（GPS）问题。改进的神经元模型在描述神经元的生物学特性方面具有优势，因此表现出复杂的放电行为。此外，我们考虑了神经元模型的非线性和不确定性参数以及未知的外部干扰，这使得对主从神经元系统的同步控制更加困难。对于神经元的同步激发节奏，通过Lyapunov方法推导了FOEHR神经元系统的神经网络（NN）滑模算法。我们使用径向基神经网络来近似误差系统的未知非线性动力学，自适应参数对逼近误差，模型不确定性和未知外部干扰具有鲁棒性。在提出的控制方案下，主从神经系统可以在有限的时间内实现GPS，并实现对不确定参数和外部干扰的恢复能力。仿真结果表明，从动神经元的膜电位与主神经元的膜电位成比例同步，并且潜在的同步误差收敛于任意小的零邻域。