This paper presents various sufficient conditions for asymptotic flocking in the relativistic Cucker–Smale (RCS) model with time delay. This model considers a self-processing time delay. We reduce the time-delayed RCS model to its dissipative structure for relativistic velocities. Then, using this dissipative structure, we demonstrate several sufficient frameworks in terms of the initial data and system parameters for asymptotic flocking of the proposed model.

This paper presents several sufficient frameworks for a collision avoidance and flocking dynamics of the Cucker–Smale (CS) model and thermodynamic CS (TCS) model with arbitrary dimensions and singular interaction kernels. In general, unlike regular kernels, singular kernels usually interfere with the global well-posedness of the targeted models from the perspective of the standard Cauchy–Lipschitz theory due to the possibility of a finite-in-time blow-up. Therefore, according to the intensity of the singularity of a kernel (strong or weak), we provide a detailed framework for the global well-posedness and emergent dynamics for each case. Finally, we provide an admissible set in terms of system parameters and initial data for the uniform stability of the $d$-dimensional TCS with a singular kernel, which can be reduced to a sufficient framework for the uniform stability of the $d$-dimensional CS with singular kernel if all agents have the same initial temperature.