Related papers: Viable harvest of monotone bioeconomic models

We consider sustainable management issues formulated within the framework of control theory. The problem is one of controlling a discrete--time dynamical system (e.g. population model) in the presence of state and control constraints,…

In natural resource management, decision-makers often aim at maintaining thestate of the system within a desirable set for all times.For instance, fisheries management procedures include keeping thespawning stock biomass over a critical…

This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known…

We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation…

The pressure on marine renewable resources has rapidly increased over past decades. The resulting scarcity has led to a variety of different control and surveillance instruments. Often they have not improved the current situation, mainly…

In this paper we address the collective management of environmental commons with multiple usages in the framework of the mathematical viability theory. We consider that the stakeholders can derive from the study of their own socioeconomic…

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…

We analyze a bioeconomic model for optimal fishery harvesting in a spatially heterogeneous habitat comprising both harvestable and preservation (reserve) zones. The population dynamics are governed by a hybrid system coupling continuous…

What determines biodiversity in nature is a prominent issue in ecology, especially in biotic resource systems that are typically devoid of cross-feeding. Here, we show that by incorporating pairwise encounters among consumer individuals…

Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…

In this manuscript we investigate the long-term behavior of a single-species fishery, which is harvested by several fleets. The time evolution of this population is modeled by a discrete time stochastic age-structured model. We assume that…

Managing infectious diseases is a world public health issue, plagued by uncertainties. In this paper, we analyze the problem of viable control of a dengue outbreak under uncertainty. For this purpose, we develop a controlled Ross-Macdonald…

We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…

In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…

Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…

In marine management, fish stocks are often managed on a stock-by-stock basis using single-species models. Many of these models are based upon statistical techniques and are good at assessing the current state and making short-term…

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…

This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…