Related papers: Border Collision Bifurcations in n-Dimensional Pie…

We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of…

For every even number $n$, and every $n$-dimensional smooth hypersurface of $\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…

We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…

We study the dynamics of the one-dimensional quasi-affine map $x\mapsto \left\lfloor \lambda x +\mu \right\rfloor$, providing a complete description of the map's periodic points, and of the limit points of every $x\in\mathbb{R}$ under the…

The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…

We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new…

We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence…

We consider the family of piecewise linear maps $F(x,y)=\left(|x| - y + a, x - |y| + b\right),$ where $(a,b)\in \R^2$. In previous work, we identified a novel phenomenon: certain maps of this class possess one-dimensional invariant sets,…

We consider the non-crossing connectors problem, which is stated as follows: Given n simply connected regions R_1,...,R_n in the plane and finite point sets P_i subset of R_i for i=1,...,n, are there non-crossing connectors y_i for…

We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…

For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce…

There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…

We propose an algorithm based on Newton's method and subdivision for finding all zeros of a polynomial system in a bounded region of the plane. This algorithm can be used to find the intersections between a line and a surface, which has…

This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…