How random immigration impacts order–chaos transformations and extinction in population dynamics

Motivated by important ecological applications, we study how immigration and noise can drastically change patterns of behavior of population systems. We explore this problem on the base of the Ricker conceptual population model and focus on two questions: (i) how random immigration can change regular and chaotic dynamic regimes of survival; (ii) how random disturbances cause extinction of population. For the initial deterministic model, we overview the variety of dynamic regimes and their transformations depending on the growth rate and intensity of immigration. For the stochastic model that takes into account random fluctuations in immigration intensity, probabilistic mechanisms for transforming order into chaos are identified and the key role of chaotic transients is revealed. A parametric study of the important population phenomenon of noise-induced extinction is given. For mathematical study of the considered stochastic deformations, a new approach based on confidence domains for regular and chaotic attractors was proposed and successfully applied.