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

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 12; p. 1329
Main Authors Ryashko, Lev, Alexandrov, Dmitri V., Bashkirtseva, Irina
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2021
Subjects
Attractors (mathematics)
climate–vegetation model
Cold
Dynamic models
Equilibrium
Food science
Freezing
Noise
Noise generation
Nonlinear systems
phantom attractor
Probability theory
Simulation
slow-fast dynamics
stochastic disturbances
Stochastic models
Time series
Vegetation
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9121329