Stochastically driven transitions between climate attractors

Abstract

A B S T R A C TThe classical non-linear climatic model previously developed by Saltzman with co-authors and Nicolis is analysed in both the deterministic and stochastic cases in a wider domain of system parameters. A detailed analysis of the deterministic model shows a co-existence of a stable cycle and equilibrium phase points of the climate system localisation. A fine structure of attraction basins existing around stable equilibria is studied. The model under consideration possesses the noise-induced transitions between possible system attractors (limit cycle and two equilibria) in the case of stochastic dynamics caused by temperature fluctuations. A new phenomenon of stochastic generation of large amplitude oscillations around two equilibrium points in the absence of a limit cycle is revealed. The co-existence of large-, small-and mixed-mode stochastic transitions between the climate system attractors is found.

Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals

“…However, it is well known that when the system parameters are near a critical state, noise can lead to dramatic changes in the observed behaviour, called noise-induced transitions in Horsthemke & Lefever [14]. Noise-induced phenomena have been observed in many models of real systems, such as a climate model [1]. However, perhaps the best known example is an excitable biological neuron with its various dynamical models, such as [11], which produce…”

“…The main contributions of the paper start in Sect. 4 where the continuity of the vector field a, considered as the solution of the ODE (2), in the input is established along with the corresponding continuity of the solution x of the ODE (1). Then in Sect.…”

Analysis of stochastic model for non-linear volcanic dynamics

“…Many uncertainties in physical parameters of volcanic dynamics (Woo, 2000) lead to a conclusion that like the climate systems (see, among others, Saltzman, 2002;Alexandrov et al, 2014), volcanoes, representing stochastic and chaotic systems, need to be described in terms of probabilities (Sparks, 2003;Bebbington and Marzocchi, 2011). Stochastic approaches and mathematical formalisms can be found in Gardiner (2009).…”

“…It is well-known, that an interplay between nonlinearity and noise can generate various probabilistic phenomena such as noise-induced transitions (Horsthemke and Lefever, 1984), stochastic resonance (McDonnell et al, 2008;Pikovsky and Kurths, 1997;Arathi, 2013), and noiseinduced chaos (Lai and Tél, 2011;Bashkirtseva et al, 2012). Stochastic effects in nonlinear models are the subjects of intensive investigations in various research domains (Horsthemke and Lefever, 1984;Lindner et al, 2004;Alexandrov et al, 2013).…”

Analysis of stochastic model for nonlinear volcanic dynamics

“…Many uncertainties in physical parameters of volcanic dynamics (Woo, 2000) lead to a conclusion that like the climate systems (see, among others, Saltzman, 2002;Alexandrov et al, 2014), volcanoes, representing stochastic and chaotic systems, need to be described in terms of probabilities (Sparks, 2003;Bebbington and Marzocchi, 2011). Stochastic approaches and mathematical formalisms can be found in Gardiner (2009).…”