Open AccessExponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance
Author(s) -
Yipeng Chen,
Yicheng Liu,
Xiao Wang
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2021023
Subject(s) - social connectedness , mathematics , flocking (texture) , piecewise , exponential function , particle system , stochastic differential equation , pure mathematics , control theory (sociology) , mathematical analysis , computer science , physics , quantum mechanics , control (management) , artificial intelligence , psychology , psychotherapist , operating system
In this paper, a generalized Motsch-Tadmor model with piecewise interaction function is investigated, which can be viewed as a generalization of the model proposed in [ 9 ]. Our analysis bases on the connectedness of the underlying graph of the system. Some sufficient conditions are presented to guarantee the system to achieve flocking. Besides, we add a stochastic disturbance to the system and consider the flocking in the sense of expectation. As results, some criterions to the flocking solution with exponential convergent rate are established by the standard differential equations analysis.