演講者：Dr. Alejandro López-Nieto
              國立臺灣大學數學系

日　期：2023 年 11 月 22 日（星期三）14:30

地　點：國立高雄大學理學院408室

講　題：The global dynamics of enharmonic oscillators

摘   要：

Discrete-time delays often arise in real-world problems, such as maturation times in population dynamics, time-delayed feedback loops in laser devices, and heat transfer lags in atmospheric models. Mathematically, delay differential equations (DDEs) produce dynamics in an infinite-dimensional phase space and contain complicated dynamics. In the talk, I will present the main result of my doctoral work [1] by introducing the enharmonic oscillator, a scalar DDE of the special form

 Here Ω  is a positive nonlinear frequency function and f is assumed to decrease monotonically in the delayed component, i.e., ∂₂f < 0.

Our main conclusion is that, the structure of the maximal compact invariant set  can be described in detail. More precisely,  possesses a graph structure whose vertices correspond to periodic or stationary solutions of the delay equation and whose edges represent heteroclinic orbits connecting the vertices. We conclude that the frequency Ω  contains the connection graph and provides an explicit method to recover the connectivity.

References

[1]  L´opez-Nieto, A.: Enharmonic motion: Towards the global dynamics of negative delayed feedback. Dissertation, Freie Universität Berlin (2023),

  http://dx.doi.org/10.17169/refubium-40043.