Analysis, Geometry, and Dynamical Systems Seminar   RSS

12/04/2018, 11:30 — 12:30 — Room P3.10, Mathematics Building
Anastasiia Panchuk, Academia Nacional das Ciências de Kiev

A piecewise linear map with two discontinuities: bifurcation structures in the chaotic domain

In the current work we consider a one-dimensional piecewise linear map with two discontinuity points and describe different bifurcation structures observed in its parameter space. The structures associated with periodic orbits have been extensively studied before (see, e.g., Sushko et al., 2015 or Tramontana et al., 2012, 2015). By contrast, here we mainly focus on the regions associated with robust multiband chaotic attractors. It is shown that besides the standard bandcount adding and bandcount incrementing bifurcation structures, occurring in maps with only one discontinuity, there also exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

  1. Sushko I., Tramontana F., Westerhoff, F. and Avrutin V. (2015): Symmetry breaking in a bull and bear financial market model. Chaos, Solitons and Fractals, 79, 57-72.
  2. Tramontana, F., Gardini L., Avrutin V. and Schanz M. (2012): Period Adding in Piecewise Linear Maps with Two Discontinuities. International Journal of Bifurcation & Chaos, 22(3) (2012) 1250068 (1-30).
  3. Tramontana, F., Westerhoff, F. and Gardini, L. (2015): A simple financial market model with chartists and fundamentalists: market entry levels and discontinuities. Mathematics and Computers in Simulation, Vol. 108, 16-40.