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Noise-induced behavioral change driven by transient chaos

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  • Jungeilges, Jochen
  • Pavletsov, Makar
  • Perevalova, Tatyana

Abstract

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.

Suggested Citation

  • Jungeilges, Jochen & Pavletsov, Makar & Perevalova, Tatyana, 2022. "Noise-induced behavioral change driven by transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s096007792200279x
    DOI: 10.1016/j.chaos.2022.112069
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    as
    1. Robin Cowan & William Cowan & G.M. Peter Swann, 2004. "Waves in consumption with interdependence among consumers," Canadian Journal of Economics, Canadian Economics Association, vol. 37(1), pages 149-177, February.
    2. Brock, W.A. & Durlauf, S.N., 1995. "Discrete Choice with Social Interactions I: Theory," Working papers 9521, Wisconsin Madison - Social Systems.
    3. McCarthy, Michael D, 1974. "On the Stability of Dynamic Demand Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 256-259, February.
    4. Gustav Feichtinger & Cars Hommes & Alexandra Milik, 1997. "Chaotic consumption patterns in a simple2-D addiction model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 147-173.
    5. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.
    6. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    7. Hammond, Peter J., 1976. "Endogenous tastes and stable long-run choice," Journal of Economic Theory, Elsevier, vol. 13(2), pages 329-340, October.
    8. H. Leibenstein, 1950. "Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 64(2), pages 183-207.
    9. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    10. Dockner, Engelbert J & Feichtinger, Gustav, 1993. "Cyclical Consumption Patterns and Rational Addiction," American Economic Review, American Economic Association, vol. 83(1), pages 256-263, March.
    11. Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    12. Granovetter, Mark & Soong, Roland, 1986. "Threshold models of interpersonal effects in consumer demand," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 83-99, March.
    13. Xu, Junyan & Zhang, Tonghua & Song, Keying, 2020. "A stochastic model of bacterial infection associated with neutrophils," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    14. Gaertner, Wulf & Jungeilges, Jochen, 1988. "A non-linear model of interdependent consumer behaviour," Economics Letters, Elsevier, vol. 27(2), pages 145-150.
    15. Pollak, Robert A., 1976. "Habit formation and long-run utility functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 272-297, October.
    16. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
    17. Rustichini, Aldo & Siconolfi, Paolo, 2014. "Dynamic theory of preferences: Habit formation and taste for variety," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 55-68.
    18. Corneo, Giacomo & Jeanne, Olivier, 1997. "Snobs, bandwagons, and the origin of social customs in consumer behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 32(3), pages 333-347, March.
    19. Jungeilges, Jochen & Ryazanova, Tatyana, 2019. "Transitions in consumption behaviors in a peer-driven stochastic consumer network," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 144-154.
    20. Becker, Gary S & Murphy, Kevin M, 1988. "A Theory of Rational Addiction," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 675-700, August.
    21. Jess Benhabib & Richard H. Day, 1981. "Rational Choice and Erratic Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 459-471.
    22. Hayakawa, Hiroaki & Venieris, Yiannis P, 1977. "Consumer Interdependence via Reference Groups," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 599-615, June.
    23. Pollak, Robert A, 1970. "Habit Formation and Dynamic Demand Functions," Journal of Political Economy, University of Chicago Press, vol. 78(4), pages 745-763, Part I Ju.
    24. Rauscher, Michael, 1992. "Keeping up with the Joneses : Chaotic patterns in a status game," Economics Letters, Elsevier, vol. 40(3), pages 287-290, November.
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