Emergent behaviors of thermodynamic Cucker–Smale ensemble with a unit-speed constraint
Hyunjin Ahn
Abstract
We propose the thermodynamic Cucker–Smale system with unit-speed constraints (TCSUS) and study its emergent dynamics with rigorous proofs. For this, three dissipative differential inequalities are derived in terms of $ L^\infty $-diameters of the position–velocity–temperature to verify mono-cluster flocking in the TCSUS model under suitable frameworks using two approaches. Motivated by the first approach, we provide a sufficient framework for bi-cluster flocking to the TCSUS model. Unlike to the mono-cluster flocking behavior of TCSUS, the decay rate of velocity–temperature for each cluster group is not exponential and is dependent on the decay rate of the corresponding communication weight, respectively.
Topics & Concepts
Flocking (texture)Dissipative systemCluster (spacecraft)Statistical physicsMathematical proofComputer scienceMathematicsPhysicsApplied mathematicsThermodynamicsGeometryProgramming languageQuantum mechanicsNonlinear Dynamics and Pattern FormationAdvanced Thermodynamics and Statistical MechanicsEvolutionary Game Theory and Cooperation