A bang–bang regime in optimal harvesting of size-structured populations

Hritonenko, Natali; Yatsenko, Yuri; Goetz, Renan-Ulrich; Xabadia, Angels

doi:10.1016/j.na.2009.05.070

Cited by 24 publications

(23 citation statements)

References 6 publications

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“…We would like to point out that the model [10,17] assumesl = l m . The model (1)-(6) atl = l m has a major drawback that will appear during further analysis of the dual problem (see Remark 1 in Section 5).…”

Section: On the Structure Of Solutionmentioning

confidence: 99%

“…Speaking mathematically, a bang-bang structure of harvesting efforts u reflects selective logging when all trees with a certain diameter are to be harvested. Bang-bang principles for age-structured models are proven in [6,13,18] and for size-structured models in [14,17]. Following [17], the strong bang-bang principle is valid for (1)- (6): If Equation (17) holds and…”

Section: On the Structure Of Solutionmentioning

confidence: 99%

“…The qualitative behaviour of the steady-state trajectory x(l) is not clear because both the numerator and denominator of Equation (26) approach zero at l →l under the growth law (17). Let us find its first derivative:…”

Section: Qualitative Dynamics Of the Steady Statementioning

confidence: 99%

“…Section 3 states that the steady-state optimal management regime u * (l) in the OCP (1)-(6) under conditions (17) and (19) is…”

Section: Steady-state Analysis Of the Ocpmentioning

confidence: 99%

“…The considered optimal control problem (OCP) maximizes the net benefits from timber production. Similar size-structured models of forest dynamics are commonly used in describing optimal forest management [7,9,10,16,17].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal harvesting in forestry: steady-state analysis and climate change impact

Hritonenko

Yatsenko

Goetz

et al. 2013

Journal of Biological Dynamics

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We perform the steady-state analysis of a nonlinear partial differential equation model that describes the dynamics of a managed size-structured forest. The harvesting policy is to maximize the net benefits from timber production over an infinite planning horizon. The existence and uniqueness of the steady-state trajectories are analysed. Closed-form steady states are obtained in meaningful special cases and are used to estimate how climate change affects the optimal harvesting regime, diameter of cut trees, number of logged trees, and net benefits in the long run.

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Section: On the Structure Of Solutionmentioning

confidence: 99%