Busy Dogs: a class of iteration problems

Haymond, R. E.; Thomas, Edward S.

doi:10.1080/10236199608808059

Cited by 1 publication

(4 citation statements)

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“…In [36], this time in an opinion dynamics framework, agents look for a mediation between their positions in an adaptive perspective. Thus, both in [28,36] a sort of bandwagon behaviour can be observed, while the snob attitude can be witnessed in [28] only. Moreover, non-constant pursuit strategies in [28] and the endogenous reactivity assumption in [36] lead to nonlinear systems, in which chaotic dynamics can emerge.…”

Section: Introductionmentioning

confidence: 95%

“…Thus, both in [28,36] a sort of bandwagon behaviour can be observed, while the snob attitude can be witnessed in [28] only. Moreover, non-constant pursuit strategies in [28] and the endogenous reactivity assumption in [36] lead to nonlinear systems, in which chaotic dynamics can emerge. Finally, we stress that, rather than considering stable preferences as we do, it is possible to deal with preference adjusting consumers, like in [22][23][24][25][26]33], where cycles are found in a model with agents having globally interdependent preferences.…”

Section: Introductionmentioning

confidence: 95%

“…On the other hand, differently from those papers, the binary choice here occurs between preference structures that characterize the two groups of agents, which are embedded in a general equilibrium framework where a price mechanism operates. Two further works which bear some resemblance to our setting are [28,36]. Namely, in [28] a class of pursuit problems is proposed, in which a decision-maker reacts in an adaptive manner to the choices of the other agent, which tries to run away, in view of reducing the distance between them.…”

Section: Introductionmentioning

confidence: 99%

“…Two further works which bear some resemblance to our setting are [28,36]. Namely, in [28] a class of pursuit problems is proposed, in which a decision-maker reacts in an adaptive manner to the choices of the other agent, which tries to run away, in view of reducing the distance between them. In [36], this time in an opinion dynamics framework, agents look for a mediation between their positions in an adaptive perspective.…”

Section: Introductionmentioning

confidence: 99%

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Fashion cycle dynamics induced by agents' heterogeneity for generic bell-shaped attractiveness functions

Naimzada

Pireddu

2019

Journal of Difference Equations and Applications

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We extend the exchange economy evolutionary discrete-time model with heterogeneous agents introduced in 'Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences', by A. Naimzada and M. Pireddu, appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 055907 (2018), by considering generic bell-shaped attractiveness functions for the two groups of agents, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The reproduction level of a group is related to its attractiveness degree, which depends on its social visibility level, determined by the consumption choices of the agents in that group. We investigate the asymptotic heterogeneity among agents, finding that the global dynamics may differ according to the chosen functional form for the attractiveness. Nonetheless, the model is still able to reproduce the recurrent dynamic behaviour typical of the fashion cycle.

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