Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control

Brock, William A.; Xepapadeas, Anastasios

doi:10.1016/j.jedc.2007.08.005

Cited by 87 publications

(78 citation statements)

References 30 publications

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“…In contrast to Boucekkine et al (2009), Brock and Xepapadeas (2008a,b and 2010, and Xepapadeas (2010), we prove the existence and unicity of a social optimum, i.e., our problem is well-posed. We provide the corresponding Pontryagin conditions, which turn out to be necessary and sufficient.…”

Section: Introductionmentioning

confidence: 69%

“…In this regard, we adapt the algorithm developed in Camacho et al (2008). This is an alternative method to the linear quadratic approximation of Brock and Xepapadeas (2008a,b and 2010, which allows us to provide global dynamics results.…”

Section: Discussionmentioning

confidence: 99%

“…In Brock and Xepapadeas (2008b) there is technological diffusion since aggregated neighbouring capital affects the location's production. Xepapadeas (2008a and2010) and Xepapadeas (2010) study the concept of diffusion in an environmental context, focusing on state variables that diffuse over the space. In particular, they find that diffusion-induced instability may create spatial patterns in infinite horizon optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

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Land use dynamics and the environment

Camacho

Pérez-Barahona

2015

Journal of Economic Dynamics and Control

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We build a model to study optimal land use, encompassing land use activities, pollution and climate change. This benchmark set-up allows us to identify the spatial drivers behind the interaction between land use and the environment.Pollution generates local and global damages since it flows across locations following a Gaussian Plume. In contrast to the previous literature on spatial dynamics, we prove that the social optimum problem is well-posed, i.e., the solution exists and is unique. We close the paper with a numerical analysis which illustrates the richness of our model, and its global dynamics. We study the different drivers of spatial heterogeneity. In particular, abatement technology stands out as a fundamental ingredient to achieve steady state solutions, which are compatible with the emergence of spatial patterns.

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Section: Introductionmentioning

confidence: 69%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Land use dynamics and the environment

Camacho

Pérez-Barahona

2015

Journal of Economic Dynamics and Control

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“…2 Reaction-diffusion systems, that is dynamical systems where the state variables interact among each either and at the same time diffuse 3 in space, have been among the main analytical tools for analyzing pattern formation in this context. A classical example is the so-called Turing mechanism (Turing 1952) which provides a framework predicting the emergence of heterogeneous spatial patterns in reaction-diffusion systems.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems

Brock

Xepapadeas

2008

SSRN Journal

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We develop a novel theoretical framework for studying ecosystems in which interacting state variables which are affected by management decisions diffuse in space. We identify (i) mechanisms creating spatial patterns when economic agents maximize profit at each site by ignoring the impact of their actions on other sites and (ii) a diffusion induced externality. Pattern formation mechanisms and externalities create a divergence in the spatiotemporal structures emerging under private or social objectives We develop optimal regulation which internalize the spatiotemporal externalities. Our theory is applied to the management and regulation of a semi-arid system. Supporting numerical simulations are also presented.

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“…Problem (134) which has been studied by Derzko et al (1984), Brock and Xepapadeas (2008), and Brock, Xepapadeas, and Yannacopoulos (2014b), has a Hamiltonian representation:…”

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confidence: 99%

Modeling Coupled Climate, Ecosystems, and Economic Systems

Brock

Xepapadeas

2015

SSRN Journal

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Human economies and ecosystems form a coupled system coevolving in time and space, since human economies use ecosystems services and at the same time a¤ect ecosystems through their production and consumption activities. The study of the interactions between human economies and ecosystems is fundamental for the e¢ cient use of natural resources and the protection of the environment. This necessitates the development and use of models capable of tracing the main interactions, links and feedbacks. In developing this chapter, our objective was to focus on a segment of rapidly developing literature on coupled ecological/economic models with an emphasis on climate change. The advantage of this approach is that it introduces the reader to a very important current research topic, but it also allows, by using climate as the reference ecosystem, the exploration of new modeling approaches which are relevant and useful for the modeling of other types of coupled ecological/economic systems. These include modeling of deep structural uncertainty by using robust control methods, exploring modeling through cumulative carbon budgeting, studying spatial transport phenomena and spatial aspects in economic/ecological modelling.

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Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control

Cited by 87 publications

References 30 publications

Land use dynamics and the environment

Land use dynamics and the environment

Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems

Modeling Coupled Climate, Ecosystems, and Economic Systems

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