Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics

Dmitri V. Alexandrov¹  Lev Ryashko¹  Irina Bashkirtseva¹ 

[1] Department of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, Russia;

关键词: phantom attractor;    stochastic disturbances;    climate–vegetation model;    slow-fast dynamics;   

DOI  :  10.3390/math9121329

来源: DOAJ

【 摘 要 】

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

【 授权许可】

Unknown