On the Role of Frustration in Couplex Dynamical Systems

点击翻译按钮获取中文摘要

In the context of physics the notion of frustration was introduced for spin systems. In this project we want to extend the concept of frustration to dynamical systems that do not derive from an action or Hamiltonian and study frustration in its various realizations. Such systems are generic oscillators, excitable media, and coupled maps. We shall study the role of frustrated units as building blocks in bi-and multistable systems in hierarchically organized systems. In analogy to spin systems, we expect an enrichment of the phase space of attractors, both in quantitative and qualitative terms, and longer relaxation times to reach a stationary state as remnant of glass-like behavior. Different attractors may be related to different functions. Well functioning biological systems perform efficiently if they are stable and flexible at the same time. Our conjecture is that an appropriate intermediate degree of frustration can achieve this goal. While a high degree of frustration makes the system unstable against perturbations, a too low degree makes it stiff and vulnerable against removal of functional units. Related to the aspect of flexibility we further expect that designing systems with a certain number of frustrated units on each level of a hierarchical organization is an efficient way of ensuring a rich phase space and a high flexibility in performance, without the need for complex units on the individual level. The project of the PhD thesis should yield results towards verification of these conjectures. While the first part will deal with the generic concept of frustration in various dynamical systems, the second part shall focus on spatially organized, genetic systems of coupled repressors and activators and study their phase space as well as their stability properties with respect to different type of perturbations in detail.