Non-emergence of mono-cluster flocking and multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint

Abstract

<abstract><p>This paper demonstrates several sufficient frameworks for the mono-cluster flocking, the non-emergence of mono-cluster flocking and the multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint (say TCSUS). First, in a different way than <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup>, we present the admissible data for the mono-cluster flocking of TCSUS to occur. Second, we prove that when the coupling strength is less than some positive value, mono-cluster flocking does not occur in the TCSUS system with an integrable communication weight. Third, motivated from the study on coupling strengths where the mono-cluster flocking does not occur, we investigate appropriate sufficient frameworks to derive the multi-cluster flocking of the TCSUS system.</p></abstract>