Related papers: Convergence results for continuous-time dynamics a…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
The paper addresses the synchronization of multi-agent systems with continuous-time dynamics interacting through a very general class of monotonic continuous signal functions that covers estimation biases, approximation of discrete…
In 2002, Chowdhury et al. introduced a simplified model aimed at depicting the dynamics of single-lane unidirectional ant traffic. Despite efforts, an exact solution for the stationary state of this ant-trail model remains elusive. The…
Navigation through narrow passages during colony relocation by the tandem-running ants, $\textit{Diacamma}$ $\textit{indicum}$, is a tour de force of biological traffic coordination. Even on one-lane paths, the ants tactfully manage a…
The asymptotically optimal version of Rapidly-exploring Random Tree (RRT*) is often used to find optimal paths in a high-dimensional configuration space. The well-known issue of RRT* is its slow convergence towards the optimal solution. A…
In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
In this study, we synthesize a novel dynamical approach for ant colonies enabling them to migrate to new nest sites in a self-organizing fashion. In other words, we realize ant colony migration as a self-organizing phenotype-level…
In this paper, we consider a nonlocal advection model for two populations on a bounded domain. The first part of the paper is devoted to the existence and uniqueness of solutions and the associated semi-flow properties. Here we use the…
Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is…
The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer…
We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…
In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application…