Effect of Visual Field in the Cucker-Smale Flocking Model

Abstract We study an extension of the classical Cucker-Smale model by introducing a visual field into the interaction mechanism through the characteristic function, which captures directional and asymmetric perception among agents. For both discrete and continuous time systems, we derive sufficient conditions for flocking, showing that convergence emerges under suitable assumptions on the initial configuration and system parameters only. We further show that these conditions reduce to the classical Cucker-Smale results in the limiting case which means that the visual field of each agent turns to $$2\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> under some initial assumptions. Numerical simulations are finally provided to illustrate our theoretical results.