Chimera states have been studied in 1D arrays, and a variety of different chimera states have been found using different models. Research has recently been extended to 2D arrays but only to phase models of them. Here, we extend it to a nonphase model of 2D arrays of neurons and focus on the influence of nonlocal coupling. Using extensive numerical simulations, we find, surprisingly, that this system can show most types of previously observed chimera states, in contrast to previous models, where only one or a few types of chimera states can be observed in each model. We also find that this model can show some special chimera-like patterns such as gridding and multicolumn patterns, which were previously observed only in phase models. Further, we present an effective approach, i.e., removing some of the coupling links, to generate heterogeneous coupling, which results in diverse chimera-like patterns and even induces transformations from one chimera-like pattern to another.
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