A dynamical system representation of generalized Rastall gravity

In this work we study the phase-space analysis of generalized Rastall gravity (GRG) which has recently been introduced as a modification to original version (RG). GRG, coupling parameter assumes dynamical feature and may play role dark energy (DE) is responsible for present accelerating expansion Universe. Our investigation shows that such General Relativity (GR) admits stable critical point corresponding late time accelerated Assuming both matter (DM) an ultra-relativistic perfect fluid (radiation) cosmic ingredients, find underlying model presents viable sequence evolution, beginning from radiation dominated era passing then through DM domination finally reaches DE era. Moreover, taking into account contribution due spatial curvature within total density leads growing mode it in way its values are consistent with those reported recent observations. We also numerical simulation particularizes our system representation. These studies demonstrate ability GRG describe