Related papers: Dynamical Systems in Elliptical Pursuit and Evasio…
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of…
We propose a combined analytical-numerical strategy to predict the dynamics and trajectory of a microswimmer next to a curved spherical obstacle. The microswimmer is actuated by a slip velocity on its surface and a uniformly valid solution…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
This paper examines the degree to which an evader seeking a safe and efficient path to a target location can benefit from increasing levels of knowledge regarding one or more range-limited pursuers seeking to intercept it. Unlike previous…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
This paper extends the family of gap-based local planners to unknown dynamic environments through generating provable collision-free properties for hierarchical navigation systems. Existing perception-informed local planners that operate in…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
We consider the system of a two ball automatic dynamic balancer attached to a rotating disc with nonconstant angular velocity. We directly compare the scenario of constant angular velocity with that when the acceleration of the rotor is…
We present a two dimensional model of hydrodynamic interaction between a circular swimmer and a circular post at low Reynolds number, using a point singularity description of the swimming activity. We derive a nonlinear dynamical system…
This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous…
Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors. A prohibitively large number of randomly placed sensors…
We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple…
This paper proposes a new perspective on the conventional planar target tracking problem. One evader and one pursuer are considered in the dynamics. In the planar tracking, pursuer has the ability to measure the position and the velocity…
A defender-attacker-target problem with non-moving target is considered. This problem is modeled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional. In this game the pursuer is the defender,…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…