2D discontinuous piecewise linear map: Emergence of fashion cycles.

  title={2D discontinuous piecewise linear map: Emergence of fashion cycles.},
  author={Laura Gardini and I. Sushko and Kiminori Matsuyama},
  volume={28 5},
We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are… 

Dynamics of a generalized fashion cycle model

Codimension-two border collision bifurcation in a two-class growth model with optimal saving and switch in behavior

We consider a two-class growth model with optimal saving and switch in behavior. The dynamics of this model is described by a two-dimensional (2D) discontinuous map. We obtain stability conditions of

Complexity Analysis of a 2D-Piecewise Smooth Duopoly Model: New Products versus Remanufactured Products

Recent studies on remanufacturing duopoly games have handled them as smooth maps and have observed that the bifurcation types that occurred in such maps belong to generic classes like period-doubling

Bifurcation Sequences and Multistability in a Two-Dimensional Piecewise Linear Map

Bifurcation mechanisms in piecewise linear or piecewise smooth maps are quite different with respect to those occurring in smooth maps, due to the role played by the borders. In this work, we descr...

Memory effects on binary choices with impulsive agents: Bistability and a new BCB structure.

It is shown that the period adding structure, characteristic for the one-dimensional case, also persists in the two-dimensional one, and the coexistence of two attracting cycles is now possible.

A Remanufacturing Duopoly Game Based on a Piecewise Nonlinear Map: Analysis and Investigations

Abstract A remanufacturing Cournot duopoly game is introduced based on a nonlinear utility function in this paper. What we mean by remanufacturing here is that the second firm in this game receives



Neimark-Sacker Bifurcations in Planar, Piecewise-Smooth, Continuous Maps

The multipliers of a fixed point of a piecewise-smooth, continuous map may change discontinuously as the fixed point crosses a discontinuity under smooth variation of parameters, similar to the Neimark–Sacker bifurcation of a smooth map.

Calculation of bifurcation Curves by Map Replacement

This work has demonstrated that the application of Leonov's technique is not resticted to that particular bifurcation structure, and the presented map replacement approach, which is an extension of Leonova's technique, allows the analytical calculation of border-collision b ifurcation curves for periodic orbits with high periods and complex symbolic sequences using appropriate composite maps.

Center bifurcation for Two-Dimensional Border-Collision Normal Form

It is shown how periodicity regions in the parameter space differ from Arnold tongues occurring in smooth models in case of the Neimark–Sacker bifurcation, how so-called dangerous border-collision bIfurcations may occur, as well as multistability.

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation.

The present article reports the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation in the two-dimensional piecewise-linear normal form map.

Period adding structure in a 2D discontinuous model of economic growth


We examine bifurcation phenomena for continuous one-dimensional maps that are piecewise smooth and depend on a parameter μ. In the simplest case, there is a point c at which the map has no derivative

Chaotic behavior in piecewise continuous difference equations

A class of piecewise continuous mappings with positive slope, mapping the unit interval into itself is studied. Families of 1-1 mappings depending on some parameter have periodic orbits for most

Bifurcation structure in the skew tent map and its application as a border collision normal form

The goal of the present paper is to collect the results related to dynamics of a one-dimensional piecewise linear map widely known as the skew tent map. These results may be useful for the

Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals

We study the bifurcations of two parameter families of circle maps that are similar tofb,w(x)=x+w+(b/2π) sin (2πx) (mod1). The bifurcation diagram is constructed in terms of setsTr, whereTr is the