Border-Collision Bifurcations in

DJW Simpson - siam REVIEW, 2016 - SIAM
For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …

Nonsmooth one-dimensional maps: some basic concepts and definitions

I Sushko, L Gardini, V Avrutin - Journal of difference equations and …, 2016 - Taylor & Francis
The main purpose of the present survey is to contribute to the theory of dynamical systems
defined by one-dimensional piecewise monotone maps. We recall some definitions known …

Degenerate bifurcations and border collisions in piecewise smooth 1D and 2D maps

I Sushko, L Gardini - International Journal of Bifurcation and Chaos, 2010 - World Scientific
We recall three well-known theorems related to the simplest codimension-one bifurcations
occurring in discrete time dynamical systems, such as the fold, flip and Neimark–Sacker …

Bifurcation structure in the skew tent map and its application as a border collision normal form

I Sushko, V Avrutin, L Gardini - Journal of Difference Equations and …, 2016 - Taylor & Francis
The goal of the present paper is to collect the results related to dynamics of a one-
dimensional piecewise linear map widely known as the skew tent map. These results may …

[图书][B] Modeling with nonsmooth dynamics

MR Jeffrey - 2020 - Springer
As mathematics is applied to model ever new problems in engineering and the life sciences,
increasing use is being made of systems that switch between different sets of equations on …

Critical homoclinic orbits lead to snap-back repellers

L Gardini, I Sushko, V Avrutin, M Schanz - Chaos, Solitons & Fractals, 2011 - Elsevier
When nondegenerate homoclinic orbits to an expanding fixed point of a map f: X→ X, X⊆ R
n, exist, the point is called a snap-back repeller. It is known that the relevance of a snap-back …

Singularities in soft-impacting systems

S Kundu, S Banerjee, J Ing, E Pavlovskaia… - Physica D: Nonlinear …, 2012 - Elsevier
In this paper, the character of the normal form map in the neighbourhood of a grazing orbit is
investigated for four possible configurations of soft impacting systems. It is shown that, if the …

Codimension-2 border collision, bifurcations in one-dimensional, discontinuous piecewise smooth maps

L Gardini, V Avrutin, I Sushko - International Journal of Bifurcation …, 2014 - World Scientific
We consider a two-parametric family of one-dimensional piecewise smooth maps with one
discontinuity point. The bifurcation structures in a parameter plane of the map are …

Dynamical analysis of a banking duopoly model with capital regulation and asymmetric costs.

S Brianzoni, G Campisi - Discrete & Continuous Dynamical …, 2021 - search.ebscohost.com
It is well known that regulation and efficiency are two important issues on banking literature.
The goal of the paper is to analyse them through a banking duopoly model with …

Chaos, border collisions and stylized empirical facts in an asset pricing model with heterogeneous agents

M Anufriev, L Gardini, D Radi - Nonlinear Dynamics, 2020 - Springer
An asset pricing model with chartists, fundamentalists and trend followers is considered. A
market maker adjusts the asset price in the direction of the excess demand at the end of …