Emergent dynamics of the fractional Cucker-Smale model under general network topologies

Abstract

<p style='text-indent:20px;'>We study the fractional Cucker-Smale (in short, CS) model under general network topologies. In [<xref ref-type="bibr" rid="b15">15</xref>], the authors introduced the fractional CS model to see the interplay of memory effect and the flocking dynamics in the all-to-all network topology. As an extension of the previous work, we investigate under which network topologies flocking still emerges. Specifically, we first consider the symmetric network case and show that the existence of a <i>leader</i> guarantees the emergence of flocking. Furthermore, we present a framework for the non-symmetric network case where we can observe the flocking. We also conduct numerical simulations to support our theoretical results and see whether our framework gives necessary and sufficient conditions for the emergence of flocking.</p>