Related papers: Is a nonlocal diffusion strategy convenient for bi…
In green security, defenders must forecast adversarial behavior, such as poaching, illegal logging, and illegal fishing, to plan effective patrols. These behavior are often highly uncertain and complex. Prior work has leveraged game theory…
Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time…
We propose, analyze and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled reaction-diffusion $N$-species competition model with harvesting or stocking effort. The time-stepping algorithms are first and…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…
Motivated by a variety of applications in control engineering and information sciences, we study network resource allocation problems where the goal is to optimally allocate a fixed amount of resource over a network of nodes. In these…
A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…
We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…
We propose here a motivation for a mixed local/nonlocal problem with a new type of Neumann condition. Our description is based on formal expansions and approximations. In a nutshell, a biological species is supposed to diffuse either by a…
Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…
In this paper, we study the homogenization of elliptic equations that combine a local part, given by the Laplacian with Neumann boundary conditions, and its nonlocal version, defined through an integral operator with a smooth kernel. These…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…
This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…