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Transitions in consumption behaviors in a peer-driven stochastic consumer network


  • Jungeilges, Jochen
  • Ryazanova, Tatyana


We study transition phenomena between attractors occurring in a stochastic network of two consumers. The consumption of each individual is strongly influenced by the past consumption of the other individual, while own consumption experience only plays a marginal role. From a formal point of view we are dealing with a special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional non-invertible map augmented by additive and/or parametric noise. In our investigation of the stochastic transitions we rely on a mixture of analytical and numerical techniques with a central role given to the concept of the stochastic sensitivity function and the related technique of confidence domains. We find that in the case of parametric noise the stochastic sensitivity of fixed points and cycles considered is considerably higher than in the case of additive noise. Three types of noise induced transitions between attractors are identified: (i) Escape from a stochastic fixed point with converge to a stochastic k-cycle, (ii) escape from the stochastic k-cycle to a stochastic fixed point, and (iii) cases in which the consumption process moves between the respective stochastic attractors for ever. The noise intensities at which such transitions are likely to occur tend to be smaller in the case of parametric noise than with additive noise.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:144-154
    DOI: 10.1016/j.chaos.2019.07.042

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    References listed on IDEAS

    1. Harrison Hong & Jeffrey D. Kubik & Jeremy C. Stein, 2001. "Social Interaction and Stock-Market Participation," NBER Working Papers 8358, National Bureau of Economic Research, Inc.
    2. Bashkirtseva, Irina & Ryashko, Lev, 2017. "Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 573-584.
    3. Alan T. Sorensen, 2006. "Social learning and health plan choice," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 929-945, December.
    4. Gaertner, Wulf & Jungeilges, Jochen, 1988. "A non-linear model of interdependent consumer behaviour," Economics Letters, Elsevier, vol. 27(2), pages 145-150.
    5. Jochen Jungeilges & Tatyana Ryazanova, 2018. "Output volatility and savings in a stochastic Goodwin economy," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 8(3), pages 355-380, December.
    6. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2019. "Dynamics of a generalized fashion cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 135-147.
    7. Anastasiia Panchuk, 2015. "CompDTIMe: Computing one-dimensional invariant manifolds for saddle points of discrete time dynamical systems," Gecomplexity Discussion Paper Series 11, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Feb 2015.
    8. Ekaterina Ekaterinchuk & Jochen Jungeilges & Tatyana Ryazanova & Iryna Sushko, 2017. "Dynamics of a minimal consumer network with uni-directional influence," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 831-857, November.
    9. repec:rje:randje:v:37:y:2006:i:4:p:929-945 is not listed on IDEAS
    10. Jungeilges, Jochen & Ryazanova, Tatyana, 2017. "Noise-induced transitions in a stochastic Goodwin-type business cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 40(C), pages 103-115.
    11. Bashkirtseva, Irina & Ryashko, Lev, 2017. "How environmental noise can contract and destroy a persistence zone in population models with Allee effect," Theoretical Population Biology, Elsevier, vol. 115(C), pages 61-68.
    12. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
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