Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves

Border Collision Bifurcations in a Footloose Capital Model with First Nature Firms

“…As a result, under variation of a parameter we may have a transition between attracting cycles of any period or transition from an attracting cycle to multi-band chaotic attractors. Investigation of dynamical systems with a piecewise smooth function, motivated from a theoretical point of view as well as by practical applications (Nusse and Yorke 1995;Nusse et al 1994;Avrutin and Schanz 2006;Sushko et al 2006), is a central topic of many scientific works published in recent years (see also Di Bernardo et al (2008) and Zhusubaliyev and Mosekilde (2003) for survey books and references therein).…”

Period-adding and the Farey tree structure in a class of one-dimensional discontinuous nonlinear maps

“…There is an enormous literature on the study of PWS continuous maps, see, for example, [1,18,[27][28][29][30]32,[34][35][36][37][38][39][40]. It is well known from these works that the bifurcations in the one-dimensional unimodal PWL continuous maps have been completely understood.…”

Sudden transition from equilibrium stability to chaotic dynamics in a cautious tâtonnement model

“…As an example, he inserted the cautious mechanism in the simplest case of pure exchange economy introduced in the well-known works of Day (see [4]) and Day and Pianigiani ([5]). The analytical description of the model resulted expressed by a bimodal 1D continuous piecewise linear map which showed the possibility of erratic the system functions at the bifurcation value ( [24,25]). One more peculiarity of piecewise smooth maps is robustness of chaotic attractors [3], that means persistence of a chaotic attractor under parameter perturbations.…”