Abstract:Delay in feedback is inevitable in a multi-agent system due to time lags in information processing for self-organization. The well-known Cucker-Smale model incorporated with this information processing delay has been recently studied, and it was shown (at least for a two-agent system) that as long as the delay is below a threshold value, the system exhibits the flocking behavior where the agents ultimately reach the same velocity. Numerical studies however suggest that the threshold value established for the delay is not optimal, and the Cucke-Smale system remains to have the flocking property for large delay. Here, we rigorously prove that flocking behavior emerges for a large information processing delay, and we establish the relationship between the admissible size of time delay and the system's parameters and initial data.

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中文翻译：

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时滞大的植绒两人座Cucker-Smale模型

摘要：由于自组织信息处理的时间滞后，在多智能体系统中反馈的延迟是不可避免的。最近研究了带有此信息处理延迟的著名的Cucker-Smale模型，并且表明（至少对于两主体系统而言），只要延迟低于阈值，系统就会出现植绒代理最终达到相同速度的行为。但是，数值研究表明，为延迟设置的阈值不是最佳的，而Cucke-Smale系统仍然具有较大延迟的植绒特性。在这里，我们严格证明了植绒行为是由于较大的信息处理延迟而出现的，并且建立了时间延迟的允许大小与系统参数和初始数据之间的关系。

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