Emergent behaviors of a thermodynamic Cucker‐Smale flock with a time‐delay on a general digraph

We present emergent flocking dynamics of a thermodynamic Cucker‐Smale (TCS) flock on a general digraph with spanning trees under the effect of communication time‐delays. The TCS model describes a temporal evolution of mechanical and thermodynamic observables such as position, velocity and temperature of CS particles. In this paper, we study how variations in mechanical and thermodynamic variables can decay to zero along a time‐independent network with position dependent weights from initial state configuration. For this, we provide a sufficient framework for a mechanical and thermodynamical flocking in terms of initial configuration, network topology, and system parameters. We also present several numerical examples and compare them with analytical results.