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Dynamics in the transition case invertible/non-invertible in a 2D Piecewise Linear Map

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  • Gardini, Laura
  • Tikjha, Wirot

Abstract

We consider the dynamics of a family of two-dimensional piecewise linear maps at the transition between the invertible and non-invertible cases. This leads to a degeneracy consisting of a half plane which is mapped onto a straight line, the critical line LC. In these regimes the ω-limit set of the trajectories must be on the images of some segment of LC. Thus, the first return map along this line can help in defining the global dynamic behavior of the two-dimensional map. In other cases, the first return map helps in determining some attracting sets, although not the unique attractors of the two-dimensional map.

Suggested Citation

  • Gardini, Laura & Tikjha, Wirot, 2020. "Dynamics in the transition case invertible/non-invertible in a 2D Piecewise Linear Map," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
  • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302137
    DOI: 10.1016/j.chaos.2020.109813
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    References listed on IDEAS

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    1. Radi, Davide & Gardini, Laura & Avrutin, Viktor, 2014. "The role of constraints in a segregation model: The symmetric case," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 103-119.
    2. Radi, Davide & Gardini, Laura, 2015. "Entry limitations and heterogeneous tolerances in a Schelling-like segregation model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 130-144.
    3. Laura Gardini & Davide Radi, 2018. "A piecewise smooth model of evolutionary game for residential mobility and segregation," Working Papers 1802, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2018.
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