Periodic cycles of social outbursts of activity
Periodic cycles of social outbursts of activity
复制标题
社会活动爆发的周期性循环
DOI：
10.1016/j.jde.2017.09.005
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发表时间：
2018
影响因子：
2.4
通讯作者：
N. Rodríguez
中科院分区：
文献类型：
--
作者：
H. Berestycki;L. Rossi;N. Rodríguez
研究了具有时间周期源项的2× 2连续动力系统的长时间行为，其中源项为合作型或激活-抑制型.该系统最近在文献[2]中引入，以模拟社会爆发的动力学，由测量活动水平的显式场和测量有效张力的隐式场组成。该系统可以用来表示一种一般类型的现象，其中一个变量表现出自激一旦其他变量已经达到临界值。时间周期源项允许人们分析对系统的周期性外部冲击在活动爆发的动力学中所起的作用。对于合作系统，我们证明了小冲击的活动水平逐渐消失，而随着冲击强度的增加，活动水平收敛到一个正的周期解（兴奋周期）。我们进一步表明，在某些情况下，有多重激发周期。我们推导出这些结果的一个子集的激活剂-抑制剂系统。
We study the long-time behavior of a 2× 2 continuous dynamical system with a time-periodic source term which is either of cooperative-type or activator–inhibitor type. This system was recently introduced in the literature [2] to model the dynamics of social outbursts and consists of an explicit field measuring the level of activity and an implicit field measuring the effective tension. The system can be used to represent a general type of phenomena in which one variable exhibits self-excitement once the other variable has reached a critical value. The time-periodic source term allows one to analyze the effect that periodic external shocks to the system play in the dynamics of the outburst of activity. For cooperative systems we prove that for small shocks the level of activity dies down whereas, as the intensity of the shocks increases, the level of activity converges to a positive periodic solution (excited cycle). We further show that in some cases there is multiplicity of excited cycles. We derive a subset of these results for the activator–inhibitor system.