Extreme parameter sensitivity of transient persistence in spatially coupled ecological systems

This paper investigates persistence of transient dynamics depending on parameters in spatially coupled ecological systems. We emphasis that the persistence time can be obtained by populations of species or Lyapunov exponents of transient dynamics. It is found that extreme sensitive dependence of persistence on parameters occurs commonly in ecological models. A non-zero uncertainty exponent is used to characterize the high sensitivity in a reasonable parameter region. The result of a small uncertainty exponent indicates a fractal structure of transient persistence in the two-dimensional parameter space. In spite of different methods of measurement, the fractal dimensions have a good consistency. Since populations of natural communities with many coupled oscillators are often affected by disturbance of migration rates, the large probability of error in estimating persistence of transients should be concerned.