Abstract
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.
Highlights
Phantom Attractors in a Mathematical modeling and analysis of complex interrelations of climate and vegetation has attracted the attention of many researchers [1,2,3,4,5]
The paper considered the role of random disturbances in complex climate–vegetation processes based on a two-dimensional dynamical model proposed by Rombouts and Ghil
Numerical modeling revealed the effect of the generation of so-called “phantom” attractors and their oppositely directed shifts corresponding to these two types of random disturbances
Summary
Phantom Attractors in a Mathematical modeling and analysis of complex interrelations of climate and vegetation has attracted the attention of many researchers [1,2,3,4,5]. One of the well known and most effectively used is the two-dimensional model proposed by Rombouts and Ghil [6]. A new stochastic phenomenon of the localization of random states of the system away from its attractors was discovered. This phenomenon called “phantom attractor” has been observed in models of enzymatic reactions, neurodynamics [19], population dynamics [20], geophysics [21]
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