Bifurcation structures of a cobweb model with memory and competing technologies

Anna Agliari, Nicolo' Pecora, Ahmad Naimzada

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

1 Citazioni (Scopus)

Abstract

In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark–Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.
Lingua originaleEnglish
pagine (da-a)78-91
Numero di pagine14
RivistaCOMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION
Volume58
DOI
Stato di pubblicazionePubblicato - 2018

Keywords

  • Heterogeneous technologies
  • Homoclinic bifurcations
  • Invariant closed curves
  • Memory
  • Neimark-sacker bifurcation

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