Can RNN work with just one input? We have a time series data.Is it possible to create a RNN such that there is only dimenson(or feature) in data(as shown in fig1).If yes,will it identify the pattern in time series data correctly? The confusion arises because only neuron (yellow to blue in figure 2) information is passed to the output.Is it sufficient to predict a pattern in time series data?
Yes, in this case train_x and train_y both have just 1 column.  RNN learns patterns in just that variable and tries to predict next instance based on the patterns.



Usually, this is just a theoretical exercise. In real world, you will have multiple features.  

Some examples :

https://machinelearningmastery.com/time-series-prediction-lstm-recurrent-neural-networks-python-keras/

https://machinelearningmastery.com/time-series-forecasting-long-short-term-memory-network-python/