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Nancy Rodriguez (UNC-CH), Ergodic Theory & Dynamical Systems Seminar
March 21, 2017 @ 3:30 pm - 4:30 pm
Title: Periodic Cycles of Social Activity
Abstract: In this talk I will begin by introducing a 2×2 dynamical system with a time-periodic source term, which can be seen as a toy model for the dynamics
social outbursts. It 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 on the dynamics of the outburst of activity.
I will discuss why for cooperative systems when the shocks are small the level of activity dies down. On the other hand, as the intensity of the shocks increases, the level of activity converges to a positive periodic solution (excited cycle). I will also discuss the possibility that there exists multiple excited cycles. If time permits I will discuss a few results related to the activator-inhibitor system.