Physical mechanisms of the dynamical patterns and non-equilibrium processes of self-driven particles in an ASEP network affected by a finite external particle source

When confronting complexity science, complexity systems indicating evolution regularities are addressed due to their nonlinearity, uncertainty, emergence and self-organization. Among them, totally asymmetric simple exclusion process (TASEP) belonging to asymmetric simple exclusion process (ASEP) stands out as a paradigm nonlinear dynamical model depicting microscopic non-equilibrium dynamics of real active particles. Motivated by real multi-physics processes of protein motors, TASEP networks with Langmuir kinetics and finite resources are studied. Partially differential equations for boundary and bulk dynamics in stochastically regular and irregular networks are numerically calculated. Connectivity, effective interactions and concentration coefficient are found to govern system dynamics. Six kinds of density profiles are observed. Fruitful dynamical patterns of global density distributions, weight distributions of each phase, local currents, local densities and related phase diagrams are obtained, which lead to acquisitions of evolvement regularities of physical mechanisms of bulk dynamics and non-equilibrium phase transitions. Three kinds of domination mechanisms including three-phase, two-phase and single-phase dominations of global dynamics are found in irregular networks. Global dynamics gradually become high-density dominated with increasing concentration coefficient or effective attachment rate. While, they gradually become low-density dominated with increasing effective detachment rate or connectivity. However, global dynamics are found to be dominated by low and high coexistence phase in general cases of regular networks. Our work is conducive to modelling nonlinear dynamical behaviors and non-equilibrium phase transition mechanisms in mesoscopic self-driven particle systems.