@article{VilkCamposMendezetal.2022,
  author    = {Vilk, Ohad and Campos, Daniel and M{\´e}ndez, Vicen{\c{c}} and Lourie, Emmanuel and Nathan, Ran and Assaf, Michael},
  title     = {Phase transition in a non-Markovian animal exploration model with preferential returns},
  series = {Physical review letters},
  volume    = {128},
  journal   = {Physical review letters},
  number    = {14},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.128.148301},
  pages     = {7},
  year      = {2022},
  abstract  = {We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. A mean-field version of this model, first suggested by Song et al., [Modelling the scaling properties of human mobility, Nat. Phys. 6, 818 (2010)] was shown to well describe human movement data. We show that our generalized model adequately describes empirical movement data of Egyptian fruit bats (Rousettus aegyptiacus) when accounting for interindividual variation in the population. We also study the probability of visiting any site a given number of times and derive a mean-field equation. Our analysis yields a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.},
  language  = {en}
}
@article{MendezMasoPuigdellosasSandevetal.2021,
  author    = {Mendez, Vicenc and Maso-Puigdellosas, Axel and Sandev, Trifce and Campos, Daniel},
  title     = {Continuous time random walks under Markovian resetting},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {103},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.103.022103},
  pages     = {8},
  year      = {2021},
  abstract  = {We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power-law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target, and the characteristic transport exponents.},
  language  = {en}
}