stochastic generation
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Energy ◽  
2021 ◽  
pp. 123026
Author(s):  
Christos N. Dimitriadis ◽  
Evangelos G. Tsimopoulos ◽  
Michael C. Georgiadis

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva

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.


2020 ◽  
Vol 30 (16) ◽  
pp. 2030051
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko

The variability of stochastic dynamics for a three-dimensional dynamic model in a parametric zone with 2-tori is investigated. It is shown how weak Gaussian noise transforms deterministic quasiperiodic oscillations into noisy bursting. The phenomenon of stochastic generation of a phantom attractor and its shift with noise amplification is revealed. This phenomenon, accompanied by order-chaos transitions, is studied in terms of stochastic [Formula: see text]- and [Formula: see text]-bifurcations.


Author(s):  
Anthony S. Kiem ◽  
George Kuczera ◽  
Pavel Kozarovski ◽  
Lanying Zhang ◽  
Garry Willgoose

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