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RESEARCH PRODUCT
Noise-induced behavioral change driven by transient chaos
Jochen JungeilgesMakar PavletsovTatyana Perevalovasubject
CO-EXISTING ATTRACTORSVDP::Samfunnsvitenskap: 200::Økonomi: 210::Økonometri: 214General MathematicsApplied MathematicsGeneral Physics and AstronomyMULTISTABILITYBEHAVIORAL CHANGESNON-ATTRACTING CHAOTIC SETStatistical and Nonlinear PhysicsSTOCHASTIC DYNAMICSSTOCHASTIC SYSTEMSNON-ATTRACTING CHAOTIC SETSSTATISTICSVDP::Samfunnsvitenskap: 200::Økonomi: 210CHAOTIC SETSDYNAMICAL SYSTEMSNOISE-INDUCED TRANSITIONCRITICAL LINESCONSUMER BEHAVIORSTOCHASTIC MODELSCONFIDENCE REGIONFORECASTINGNOISE-INDUCED TRANSITIONSTRANSIENT CHAOSdescription
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil'shtein and Ryashko (1995) does not apply since the required exponentially stable attractor, for which a confidence region could be constructed, does not exist. To solve the prediction problem we propose a heuristic based on the idea that a vague manifestation of a non-attracting chaotic set (chaotic repellor) - could serve as a surrogate for an attractor. A representation of the surrogate is generated via an algorithm for generating the boundary of an absorbing area due to Mira et al. (1996). Then a confidence domain for the surrogate is generated using the approach due to Bashkirtseva and Ryashko (2019). The intersections between this confidence region and the immediate basins of the coexisting attractors can then be used to make predictions about transition events. Preliminary assessments show that the heuristic indeed explains the transition probabilities observed in numerical experiments. © 2022 The Authors 075-02-2022-877; Ministry of Education and Science of the Russian Federation, Minobrnauka Tatyana Perevalova and Jochen Jungeilges gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2022-877 ).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-05-01 |