Finite-in-time flocking of the thermodynamic Cucker–Smale model

Hyunjin Ahn; Se Eun Noh; Hyunjin Ahn; Se Eun Noh

doi:10.3934/nhm.2024023

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 526-546. doi: 10.3934/nhm.2024023

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Research article

Finite-in-time flocking of the thermodynamic Cucker–Smale model

Hyunjin Ahn ^,,
Se Eun Noh

Department of Mathematics, Myongji University, Gyeonggi-do 17058, Republic of Korea

Received: 27 March 2024 Revised: 26 April 2024 Accepted: 07 May 2024 Published: 16 May 2024

We illustrate finite-in-time flocking in the thermodynamic Cucker–Smale (TCS) model. First, we extend the original TCS model to allow for a continuous vector field with a locally Lipschitz continuity. Then, within this system, we derive appropriate dissipative inequalities concerning the position-velocity-temperature using several preparatory estimates. Subsequently, based on initial data and system parameters, we formulate sufficient conditions to guarantee the desired finite-time flocking in each case where the communication weight conditions are divided into two scenarios: one with a positive lower bound and another with nonnegativity and monotonicity. Finally, we provide several numerical simulations and compare them with the analytical results.
- Continuous dynamics,
- dissipative structure,
- finite-in-time flocking,
- multi-agent system,
- thermodynamic Cucker–Smale
Citation: Hyunjin Ahn, Se Eun Noh. Finite-in-time flocking of the thermodynamic Cucker–Smale model[J]. Networks and Heterogeneous Media, 2024, 19(2): 526-546. doi: 10.3934/nhm.2024023

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Abstract

We illustrate finite-in-time flocking in the thermodynamic Cucker–Smale (TCS) model. First, we extend the original TCS model to allow for a continuous vector field with a locally Lipschitz continuity. Then, within this system, we derive appropriate dissipative inequalities concerning the position-velocity-temperature using several preparatory estimates. Subsequently, based on initial data and system parameters, we formulate sufficient conditions to guarantee the desired finite-time flocking in each case where the communication weight conditions are divided into two scenarios: one with a positive lower bound and another with nonnegativity and monotonicity. Finally, we provide several numerical simulations and compare them with the analytical results.

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