Convolution neural network and recurrent neural network modeling of nonlinear dynamical systems is applicable for regression of the multivariate timeseries, which displays chaotic temporal variations between two states in the case of logistic and Lorenz dynamics. In the global correlated seismicity dynamics, it is provided that the pitchfork type bifurcation dynamics concerning the relation of rate of earth rotation and the correlated seismicity is possibly understood by the transition between global seismicity network structures under the periodic external force. In the three-arm slider-block network, it shows that the temporal variation of the multivariate timeseries appears multi-states bifurcation and supercritical bifurcation under the periodic external force, thereby suggesting that the global and regional correlated seismicity dynamics is nearly approximated to this three-arm network of the global subduction system.