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A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models

I. Mazari, D. Ruiz-Balet. A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models (2020)

Abstract. Following the recent works [9, 17, 30, 31, 37], we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a surprising fragmentation phenomenon: depending on the scale of diffusivity (i.e the dispersal rate), it is better to either concentrate or fragment resources. Our main result is that, the smaller the dispersal rate of the species in the domain, the more optimal resources distributions tend to oscillate. This is in sharp contrast with other criteria in population dynamics, such as the classical problem of optimising the survival ability of a species, where concentrating resources is always favourable, regardless of the diffusivity. Our study is completed by numerous numerical simulations that confirm our results.

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Last updated on March 17, 2022

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Last Publications

Optimal actuator design via Brunovsky’s normal form

Stability and Convergence of a Randomized Model Predictive Control Strategy

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

Control of certain parabolic models from biology and social sciences

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
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