Abstract
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.
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