Related papers: Null controllability of a cascade model in populat…
In this paper, we present a class of network topologies under which the Laplacian consensus dynamics exhibits undesirable controllability properties under a broadcast control signal. Specifically, the networks we characterize are…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain where the diffusion coefficient degenerates at one point of the…
This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…
A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with…
We study the problem of controlling population dynamics, a class of linear dynamical systems evolving on the probability simplex, from the perspective of online non-stochastic control. While Golowich et.al. 2024 analyzed the fully…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
This paper considers the controllability of a class of coupled Stokes systems with distributed controls. The coupling terms are of a different nature. The first coupling is through the principal part of the Stokes operator with a constant…
In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…
We are interested in predator-prey dynamics on infinite trees, which can informally be seen as particular two-type branching processes where individuals may die (or be infected) only after their parent dies (or is infected). We study two…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
In this paper, we study the indirect boundary stability and exact controllability of a one-dimensional Timoshenko system. In the first part of the paper, we consider the Timoshenko system with only one boundary fractional damping. We first…
We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…
The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a…