Adapting to a changing environment: non-obvious thresholds in multi-scale systems

作者:Perryman Clare*; Wieczorek Sebastian
来源:Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2014, 470(2170): 20140226.
DOI:10.1098/rspa.2014.0226

摘要

Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such %26apos;non-adiabatic%26apos; processes are ubiquitous, but little understood. We identify these processes with a new nonlinear phenomenon-an intricate threshold where a forced system fails to adiabatically follow a changing stable state. In systems with multiple time scales, we derive existence conditions that show such thresholds to be generic, but non-obvious, meaning they cannot be captured by traditional stability theory. Rather, the phenomenon can be analysed using concepts from modern singular perturbation theory: folded singularities and canard trajectories, including composite canards. Thus, non-obvious thresholds should explain the failure to adapt to a changing environment in a wide range of multi-scale systems including: tipping points in the climate system, regime shifts in ecosystems, excitability in nerve cells, adaptation failure in regulatory genes and adiabatic switching in technology.

  • 出版日期2014-10-8