One-dimensional (1D) map-based neuron models are of significant interest according to their simplicity of simulation and ability to mimic real neurons’ complex behaviors. A fractional-order 1D neuron map is proposed in this paper. Dynamical characteristics of the model are analyzed by obtaining bifurcation diagrams and the Lyapunov exponents’ diagram. Furthermore, emerging the spiral wave as one of the most important collective behaviors is studied in a 2D lattice consisting of this new FO neuron model. The outcome of changing stimuli, coupling strength, and fractional-order parameter as the effective parameters is examined in this network. Moreover, an efficient way of suppressing the spiral wave has been investigated using impulse triggering.

基于一维 (1D) 地图的神经元模型因其模拟的简单性和模拟真实神经元复杂行为的能力而备受关注。本文提出了一种分数阶一维神经元映射。通过得到分岔图和李雅普诺夫指数图，分析了模型的动力学特性。此外，在由这种新的 FO 神经元模型组成的 2D 晶格中，研究了将螺旋波作为最重要的集体行为之一出现。在这个网络中检查了改变刺激、耦合强度和分数阶参数作为有效参数的结果。此外，已经研究了使用脉冲触发来抑制螺旋波的有效方法。