Transition between order and chaos in a composite disk galaxy model with a massive nucleus and a dark matter halo

► We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk halo, a massive dense nucleus and a dark halo component. ► We obtain relationships connecting the critical value of the mass of nucleus or the critical value of the component of the angular momentum with the mass of the dark halo. ► The mass of the dark halo, the mass of the dense nucleus and the angular momentum are important physical quantities regarding the nature of the orbits in this system.