Bifurcations in one-dimensional piecewise smooth maps-theory and applications in switching circuits

By S. Banerjee, M. Karthik, Guo-Cheng Yuan, James A. Yorke. 2000

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Complex behavior in switching power converters (2002, methodology): “Analysis of current-mode controlled converters by the iterative-map approach can be found in [24], [25], and [ 29 ].”
On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders (2010, background): “The one-dimensional piecewise linear case, continuous and discontinuous, was considered by Banerjee et al. (2000); Jain and Banerjee (2003); Avrutin and Schanz (2006, 2008); Avrutin et al. (2006) and Di Bernardo et al. (2008).”
Bifurcation structure in the skew tent map and its application as a border collision normal form (2016, methodology): “2 The investigation of the dynamics of the skew tentmap, as well as of the tent map, which is defined by Equation (1) for aR = −aL, has drawn the attention of many researches from different areas of the theory of nonlinear dynamics and its applications (we refer to [4,14,16,19,21,26], to cite a few)”
Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves (2006, methodology): “In [1] it is proposed to study the border-collision phenomena by means of a so-called normal form, which is the piecewise linear approximation of the map in the neighborhood of the border point.”