Related papers: Piecewise Smooth Dynamical Systems Regularized by …
In this paper, we provide a geometric analysis of a new hysteresis model that is based upon singular perturbations. Here hysteresis refers to a type of regularization of piecewise smooth differential equations where the past of a…
Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…
The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…
We construct a series of vortex patch solutions in a doubly-periodic rectangular domain (flat torus), which is accomplished by studying the contour dynamic equation for patch boundaries. We will illustrate our key idea by discussing the…
We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence…
In this paper we study the Sotomayor-Teixeira regularization of a general visible fold singularity of a Filippov system. Extending Geometric Fenichel Theory beyond the fold with asymptotic methods, we determine there the deviation of the…
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the…
This paper studies the asymptotic behavior of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge…
In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. It is…
In this work we develop a well-defined theory of orbit spaces for piecewise smooth vector fields (PSVFs). This approach is inspired by the techniques already used in the study of endomorphisms, namely inverse limit analysis, and has been…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
In this paper, we extend the slow divergence-integral from slow-fast systems, due to De Maesschalck, Dumortier and Roussarie, to smooth systems that limit onto piecewise smooth ones as $\epsilon\rightarrow 0$. In slow-fast systems, the slow…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
The {\it two-fold singularity} has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that…
The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its…
We consider the holomorphic normalization problem for a holomorphic vector field in the neighborhood of the product of a fixed point and an invariant torus. Supposing that the vector field is a perturbation of a linear part around the fixed…
We use blowup to study the regularization of codimension one two-fold singularities in planar piecewise smooth (PWS) dynamical systems. We focus on singular canards, pseudo-equlibria and limit cycles that can occur in the PWS system. Using…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…