Nonsmooth one-dimensional maps: some basic concepts and definitions
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 …
defined by one-dimensional piecewise monotone maps. We recall some definitions known …
Bifurcation structure in the skew tent map and its application as a border collision normal form
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 …
dimensional piecewise linear map widely known as the skew tent map. These results may …
Bifurcation structures in a bimodal piecewise linear map: chaotic dynamics
In this work, we investigate the bifurcation structure of the parameter space of a generic 1D
continuous piecewise linear bimodal map focusing on the regions associated with chaotic …
continuous piecewise linear bimodal map focusing on the regions associated with chaotic …
Onset of chaos in a single-phase power electronic inverter
V Avrutin, E Mosekilde, ZT Zhusubaliyev… - … Journal of Nonlinear …, 2015 - pubs.aip.org
Supported by experiments on a power electronic DC/AC converter, this paper considers an
unusual transition from the domain of stable periodic dynamics (corresponding to the …
unusual transition from the domain of stable periodic dynamics (corresponding to the …
[HTML][HTML] Deep learning for prediction and classifying the dynamical behaviour of piecewise-smooth maps
VS Vismaya, BV Nair, SS Muni - Franklin Open, 2024 - Elsevier
This paper explores novel ways of predicting and classifying the dynamics of piecewise
smooth maps using various deep learning models. Moreover, we have used machine …
smooth maps using various deep learning models. Moreover, we have used machine …
Border collision bifurcations of chaotic attractors in one-dimensional maps with multiple discontinuities
In one-dimensional piecewise smooth maps with multiple borders, chaotic attractors may
undergo border collision bifurcations, leading to a sudden change in their structure. We …
undergo border collision bifurcations, leading to a sudden change in their structure. We …
A financial market model with two discontinuities: Bifurcation structures in the chaotic domain
We continue the investigation of a one-dimensional piecewise linear map with two
discontinuity points. Such a map may arise from a simple asset-pricing model with …
discontinuity points. Such a map may arise from a simple asset-pricing model with …
Can a border collision bifurcation of a chaotic attractor lead to its expansion?
Recently, we reported that a chaotic attractor in a discontinuous one-dimensional map may
undergo a so-called exterior border collision bifurcation, which causes additional bands of …
undergo a so-called exterior border collision bifurcation, which causes additional bands of …
Bubbling in a power electronic inverter: Onset, development and detection
V Avrutin, JD Morcillo, ZT Zhusubaliyev… - Chaos, Solitons & …, 2017 - Elsevier
Power electronic DC/AC converters (inverters) play an important role in modern power
engineering for a broad variety of applications including solar and wind energy systems as …
engineering for a broad variety of applications including solar and wind energy systems as …
Dynamics of a minimal consumer network with bi-directional influence
We study the dynamics of a model of interdependent consumer behavior defined by a family
of two-dimensional noninvertible maps. This family belongs to a class of coupled logistic …
of two-dimensional noninvertible maps. This family belongs to a class of coupled logistic …