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On the emergence and properties of weird quasiperiodic attractors

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  • Gardini, Laura
  • Radi, Davide
  • Schmitt, Noemi
  • Sushko, Iryna
  • Westerhoff, Frank

Abstract

We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our knowledge, this type of attractor, which we call a weird quasiperiodic attractor, has not yet been studied in detail. It has a rather complex geometric structure and other interesting properties that are worth exploring in more depth. To this end, we consider a simpler map that can also possess weird quasiperiodic attractors, namely, a 2D discontinuous piecewise linear map F with a single discontinuity line dividing the phase plane into two partitions, where two different homogeneous linear maps are defined. Map F depends on four parameters — the traces and determinants of the two Jacobian matrices. In the parameter space of map F, we obtain specific regions associated with the existence of weird quasiperiodic attractors; describe some characteristic properties of these attractors; and explain one of the possible mechanisms of their appearance.

Suggested Citation

  • Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2025. "On the emergence and properties of weird quasiperiodic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925009294
    DOI: 10.1016/j.chaos.2025.116916
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    References listed on IDEAS

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    1. Do, Younghae, 2007. "A mechanism for dangerous border collision bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 352-362.
    2. Zhao, Yifan & Zhang, Yongxiang, 2023. "Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2025. "On the limits of informationally efficient stock markets: New insights from a chartist-fundamentalist model," International Review of Financial Analysis, Elsevier, vol. 105(C).
    Full references (including those not matched with items on IDEAS)

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