Control of a Metapopulation Harvesting Model for Black Bears

Salinas, René; Lenhart, Suzanne; Gross, Louis J.

doi:10.1111/j.1939-7445.2005.tb00160.x

Cited by 13 publications

(8 citation statements)

References 18 publications

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“…Salinas et al [9] have proposed a similar metapopulation model with harvesting in the forest and in the park (only at a low level). They also consider the case of a periodic carrying capacity.…”

Section: F(t) Kmentioning

confidence: 98%

Optimal control of harvesting in a stochastic metapopulation model

Collins

Lenhart

Nanda

et al. 2011

Optim Control Appl Methods

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SUMMARYWe consider a metapopulation model for a single species inhabiting two bounded contiguous regions where movement of the population across the shared boundary is allowed. The population in one of the bounded regions can be harvested. We introduce stochastic growth rates for the two populations in a system of ordinary differential equations that model the population dynamics in these two regions. We derive the resulting stochastic control problem with harvesting in the one region as the control. The existence of an optimal control is established by solving an associated quasi-linear-quadratic optimal control problem. We present numerical simulations to illustrate several scenarios.

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Section: F(t) Kmentioning

confidence: 98%

Optimal control of harvesting in a stochastic metapopulation model

Collins

Lenhart

Nanda

et al. 2011

Optim Control Appl Methods

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“…The convergence of such an iterative method is based on the work of Hackbush [14]. Other examples using this method can be found in [11,16,41].…”

Section: Numerical Illustrations For Augmentation Examplementioning

confidence: 99%

Illustrating Optimal Control Applications with Discrete and Continuous Features

Lenhart

Bodine

Zhong

et al. 2013

Advances in Applied Mathematics, Modeling, and Computational Science

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In this paper, we present the basic idea of optimal control of models with discrete and continuous features. We first consider ordinary differential equation (ODE) models where we emphasize problems which are linear in the control and have discrete values for the optimal control. Three examples with ODEs illustrate how the bang-bang and singular controls could be handled. The first example utilizes a simple model with one ODE. The next two examples use systems of ODEs. One example comes from a mobile robot with one or more steerable drive wheels that steer together. The other example models species augmentation where two populations of the same species are modeled with a target/endangered population and a reserve population. Then we present an extension to an integrodifference model that is discrete in time and continuous in space. This optimal pest control problem is modeled by integrodifference equations and we illustrate how to construct the necessary conditions.

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“…Salinas et al, 2005;Burnett et al, 2007), as opposed to being invaded or non-invaded in a binary sense (as in EpanchinNiell and Wilen, 2012;Chadès et al, 2011), in a single jurisdiction setting. Additionally, we allow for a second intervention which we term containment.…”

Section: Introductionmentioning

confidence: 96%

“…Under the assumption that the invasion always arrives at one end of the line network, and spreads patch by patch through the network, a two-patch model is sufficient to analyse the optimality of removal, containment and combining both removal and containment. Two-patch models have been shown to provide useful insights in related settings by Salinas et al (2005) and Sanchirico et al (2010). We explore the effects of heterogeneity of damage costs between patches and the costs of interventions on optimal policies and thus demonstrate the added value from considering varying stock size within patches.…”

Section: Introductionmentioning

confidence: 99%