Fully nonlinear Cucker–Smale model for pattern formation and damped oscillation control.

We conduct a theoretical study of the phenomena associated with the self-organization of multi-agents with nonlinear interactions that form the desired spatial pattern without collision. To demonstrate this, we first adopt a singular Cucker–Smale model, which contains a discrete p -Laplacian (p > 1) and external control signals. Then, we introduce a range of properties for the energy function of our model and prove that the model supports non-collision, flocking, and pattern formation. In addition, we employ numerical simulations to show that, depending on the initial data and the discrete p -Laplacian, various significant effects exist, such as the speed control of pattern positioning and amplitude adjustment of damped oscillation. • Fully nonlinear Cucker–Smale model with external signals is addressed. • We prove the flocking phenomenon for the model. • We show that agents of the model induce a pattern formation according to the external signals. • We discuss that the damped oscillation phenomenon can be controlled according to the parameters. [ABSTRACT FROM AUTHOR]