Bifurcations of optimal vector fields in the shallow lake model

Tatiana Kiseleva; rnF.O.O. Wagener

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Bifurcations of optimal vector fields in the shallow lake model

机译：浅湖模型中最优矢量场的分叉

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The solution structure of the set of optimal solutions of the shallow lake problem, a problem of optimal pollution management, is studied as we vary the values of the system parameters: the natural resilience, the relative importance of the resource for social welfare and the future discount rate. We find parameter values at which qualitative changes occur. Using theoretical results on the bifurcations of the solution structure to infinite horizon optimization problems obtained earlier, we give a fairly complete bifurcation analysis of the shallow lake problem. In particular, we show how the increase of the discount rate affects the parameter regions where an oligotrophic steady state, corresponding to low pollution level, is globally stable or locally stable under optimal dynamics. Asymptotically, an increase of the discount rate can be offset with a proportional increase of the relative social weight of the resource.

机译：当我们改变系统参数的值：自然复原力，资源对社会福利的相对重要性以及未来的价值时，研究了浅湖问题的最优解集（一个最优污染管理问题）的解结构。折扣率。我们找到发生质变的参数值。使用关于较早获得的无限层位优化问题的解结构分支的理论结果，我们对浅湖问题进行了相当完整的分支分析。特别是，我们显示了折现率的提高如何影响参数区域，在这些区域中，低营养水平的寡营养稳态在最佳动力学下是全局稳定或局部稳定的。渐近地，折现率的增加可以通过资源相对社会权重的成比例增加来抵消。

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来源
《Journal of Economic Dynamics and Control》 |2010年第5期|p.825-843|共19页
作者
Tatiana Kiseleva; rnF.O.O. Wagener;
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作者单位

CeNDEF, Department of Quantitative Economics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands Tinbergen Institute, Roetersstraat 31, 1018 WB Amsterdam, The Netherlands;

rnCeNDEF, Department of Quantitative Economics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands Tinbergen Institute, Roetersstraat 31, 1018 WB Amsterdam, The Netherlands;

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正文语种 eng
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关键词
otimal vector fields; indifference points; bifurcations; shallow lake;

机译：最佳矢量场;冷漠点;分叉;浅湖;

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1. Bifurcations of Optimal Vector Fields [J] . Kiseleva Tatiana, Wagener Florian Mathematics of operations research . 2015,第1期

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2. Behavior of limit cycle bifurcations for a class of quartic Kolmogorov models in a symmetrical vector field [J] . Chaoxiong Du, Yirong Liu, Wentao Huang Applied Mathematical Modelling . 2016,第5a6期

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3. Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field [J] . Du Chaoxiong, Liu Yirong, Huang Wentao International journal of bifurcation and chaos in applied sciences and engineering . 2014,第3期

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4. Comparison between hydrostatic and non-hydrostatic 3-D modelling of wind-driven turbulent flow fields in a shallow lake [C] . G. Ciraolo, J. Jozsa, T. Kramer, International conference on hydroinformatics . 2002

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5. Local bifurcations of quadratic vector fields. [D] . Fiddelaers, Peter. 1992

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6. Numerical computation of the optimal vector field: Exemplified by a fishery model [O] . D. Grass -1

机译：最优矢量场的数值计算：以渔业模型为例
7. Bifurcations of optimal vector fields in the shallow lake model [O] . Florian Wagenerab 2015

机译：浅湖模型中最优矢量场的分支
8. Investigation of Global Bifurcations in Planar Vector Fields [R] . Guckenheimer, J. 1988

机译：平面矢量场中全局分岔的研究

Bifurcations of optimal vector fields in the shallow lake model

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