Related papers: On Planar Shadowing Curves to Closed Escaping Curv…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
We formulate and analyze a three-dimensional model of motion camouflage, a stealth strategy observed in nature. A high-gain feedback law for motion camouflage is formulated in which the pursuer and evader trajectories are described using…
There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one…
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in…
Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative…
Many synoptic surveys are observing large parts of the sky multiple times. The resulting lightcurves provide a wonderful window to the dynamic nature of the universe. However, there are many significant challenges in analyzing these light…
We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the…
This paper studies a pursuit-evasion problem involving a single pursuer and a single evader, where we are interested in developing a pursuit strategy that doesn't require continuous, or even periodic, information about the position of the…
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…
Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research…
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
Elucidating emergent regularities in intriguing crowd dynamics is a fundamental scientific problem arising in multiple fields. In this work, based on the social force model, we simulate the typical scenario of collective escape towards a…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
We show that the maximal number of singular moves required to pass between any two regularly homotopic planar or spherical curves with at most n crossings, grows quadratically with respect to n. Furthermore, this can be done with all curves…
We revisit the shadows of rotating braneworld black holes in the Randall-Sundrum type II model, by considering not only the metric in the near region of the black hole but also the linearized metric in the far region where the observer…
Given a mapped environment, we formulate the problem of visually tracking and following an evader using a probabilistic framework. In this work, we consider a non-holonomic robot with a limited visibility depth sensor in an indoor…
System identification aims to build models of dynamical systems from data. Traditionally, choosing the model requires the designer to balance between two goals of conflicting nature; the model must be rich enough to capture the system…