In this chapter, we present the Cucker–Smale-type flocking models and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies, and initial data. In 2007, two mathematicians Felipe Cucker and Steve Smale introduced a second-order particle model which resembles Newton’s equations in N-body system and present how their simple model can exhibit emergent flocking behavior under sufficient conditions expressed only in terms of parameters and initial data. After Cucker–Smale’s seminal works in [31, 32], their model has received lots of attention from applied math and control engineering communities. We discuss the state of the art for the flocking theorems to Cucker–Smale-type flocking models.
|Title of host publication||Modeling and Simulation in Science, Engineering and Technology|
|Number of pages||33|
|Publication status||Published - 2017|
|Name||Modeling and Simulation in Science, Engineering and Technology|
Bibliographical noteFunding Information:
Acknowledgements The work of S.-Y. Ha was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03. The work of Y.-P. Choi was supported by Engineering and Physical Sciences Research Council (EP/K008404/1). The work of Z. Li was supported by the National Natural Science Foundation of China Grant No.11401135, and Fundamental Research Funds for the Central Universities (HIT.BRETIII.201501 and HIT.PIRS.201610).
© Springer International Publishing AG 2017.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Fluid Flow and Transfer Processes
- Computational Mathematics