Related papers: Border Collision Bifurcations in n-Dimensional Pie…
This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stable focus transitions to an unstable focus by colliding with…
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a…
We present an algorithm that computes the girth of the intersection graph of $n$ given line segments in the plane in $O(n^{1.483})$ expected time. This is the first such algorithm with $O(n^{3/2-\varepsilon})$ running time for a positive…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
In this paper we consider a system of strongly coupled logistic maps involving two parameters. We classify and investigate the stability of its fixed points. A local bifurcation analysis of the system using Center Manifold is undertaken and…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points.…
In this paper, we study one-dimensional boundary blow up problems with Kirchhoff type nonlocal terms on an interval. We perform a bifurcation analysis on the problems and obtain the precise number of solutions according to the value of the…
The bifurcation structure of the Langford equation is studied numerically in detail. Periodic, doubly-periodic, and chaotic solutions and the routes to chaos via coexistence of double periodicity and period-doubling bifurcations are found…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…
Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the…
Developing a previous idea of Faltings, we characterize the complete intersections of codimension 2 in P^n, n>=3, over an algebraically closed field of any characteristic, among l.c.i. X, as those that are subcanonical and…
Let $\mathcal{D}$ be a set of straight-line segments in the plane, potentially crossing, and let $c$ be a positive integer. We denote by $P$ the union of the endpoints of the straight-line segments of $\mathcal{D}$ and of the intersection…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(DX\) and \(DY\) each have one nonzero…
We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows…
This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\'e--Bendixson regions by using transversal conics. We present several…