In　this　paper,　a　novel　incremental　radial　basis　function　(RBF)　neural　network　is　proposed　for　nonlinear　systems　modeling.　The　hidden　layer　is　constructed　dynamically　on　the　basis　of　the　neuronal　activity　(NA),　which　is　measured　by　the　local　field　potential　(LFP)　and　the　average　firing　rate　(AFR),　with　the　goal　of　enhancing　the　structural　compactness.　Simultaneously,　a　modified　second-order　algorithm　is　utilized　to　tram　the　neuronal　activity-based　RBF　(NARBF)　neural　network,　which　can　decrease　the　convergence　time　and　improve　the　generalization　performance.　Then,　three　benchmark　nonlinear　system　modeling　simulations　are　employed　to　evaluate　the　proposed　NARBF　neural　network,　indicating　that　the　proposed　neural　network　can　obtain　good　generalization　performance　with　a　compact　structure　after　fast　training.　Finally,　the　NARBF　neural　network　is　applied　to　wastewater　treatment　process　modeling,　which　demonstrates　that　the　proposed　algorithm　can　predict　the　key　water　quality　variable　precisely.