In the present work, we have developed a two-dimensional gravitational model of barred galaxies to analyse the fate of escaping stars from the central barred region. For that, the model has been analysed for two different bar profiles viz. strong and weak. Here the phenomena of stellar escape from the central barred region have been studied from the perspective of an open Hamiltonian dynamical system. We observed that the escape routes correspond to the escape basins of the two index-1 saddle points. Our results show that the formation of spiral arms is encouraged for the strong bars. Also, the formation of grand design spirals is more likely for strong bars if they host central super massive black holes (SMBHs). In the absence of central SMBHs, the formation of less-prominent spiral arms is more likely. Again, for weak bars, the formation of inner disc rings is more probable.
