We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, i.e. the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of the instantaneous local order parameter in two dimensions. Finally we extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of patterns' propagation in two dimensions.

我们研究了在具有局部和非局部耦合相互存在的 Hindmarsh-Rose 突发神经元二维网络中旅行嵌合体状态的出现。我们表明，在非线性函数建模的非局部化学耦合的独特存在下，移动的嵌合体现象发生在网格平面的两个方向上的位移。局部电耦合的引入表明，两种耦合类型的相互影响可以在某些值下产生旅行嵌合体、不完美旅行、旅行多簇和交替旅行嵌合体，即存在于所研究的网络中，运动中散布着其他不相干元素并随时间交替改变其位置的相干元素模式。相干状态的确认是通过在二维中引入瞬时局部阶参数的参数来完成的。最后，我们通过数学工具（如 Hamilton 能量函数）扩展我们的分析，以确定二维模式的传播方向。