Noise-induced versus intrinsic oscillations in ecological systems*

Cyclic and oscillatory behaviors are ubiquitous in ecological systems. These oscillations can be noise-induced or due to the intrinsic ecological interactions. Due to the stochastic nature of ecological systems, these types of oscillations appear to be very similar, and distinguishing between them, using ecological data, is a topic of active research. Classic discrete population models like Ricker and Logistic maps are well-known in their ability to model a wide variety of ecological systems. One of the characteristics of such maps is the famous period-doubling route to chaos. This feature provides us the opportunity to study the behavior of the system in different regimes, simply by choosing the appropriate parameter value. In the two-cycle regime and implemented on a lattice with nearest neighbor coupling, these models are shown to undergo a second order phase transition. We numerically investigated the dynamics of coupled, noisy oscillators, as we slowly change the parameter from the steady state to the two-cycle regime. Although for an individual map the steady-state is not easily distinguishable from the two-cycle regime in the presence of noise, the coupled, noisy system exhibits qualitatively different behavior in these two regimes.