| Abstract: |
| We consider a predator and a prey moving with Fractional Laplacians, letting the predator and the prey free to choose the exponent characterising the distribution of the jump lengths. Which exponent should the predator use to maximise its chance to catch the prey? And which one should the prey select to minimise the possibility of meeting the predator? In this talk, we study a funtional that describes the chance of meeting taking into account both strategies. We focus in particular on the case of a large initial distance and we find ranges for the parameter of fractional diffusion corresponding to the maximum (for the predator) and the minimum (for the prey) in dependence of the choice of the other species. These findings rely on very fine estimates of the fundamental solution of the fractional heat equation. |
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