Related papers: Boundary and Interior Control in a Diffusive Lotka…
This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each state's occurrence remain poorly understood. Here, we characterize and explain the…
The aim of this study is to analyze the integrability problem of Lotka--Volterra three species biological system. The system which considered in this work is a biological plausibility or a chemical model. The system has a complex dynamical…
We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…
A class of models of long waves in dispersive media with coupled quadratic nonlinearities on a periodic domain $\mathbb{T}$ are studied. We used two distributed controls, supported in $\omega\subset\mathbb{T}$ and assumed to be generated by…
In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global…
In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or…
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on…
In this paper, we study a three-patch two-species Lotka-Volterra competition patch model over a stream network. The individuals are subject to both random and directed movements, and the two species are assumed to be identical except for…
In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a…
We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…