Abstract
We solve an adaptive search model where a random walker or Lévy flight stochastically resets to previously visited sites on a d-dimensional lattice containing one trapping site. Because of reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which nondiffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker’s return probability in the memoryless case. The transition belongs to the same class as the self-consistent theory of Anderson localization. These results show that similarly to many living organisms and unlike the well-studied Markovian walks, non-Markov movement processes can allow agents to learn about their environment and promise to bring adaptive solutions in search tasks.
Original language | English |
---|---|
Article number | 40603 |
Number of pages | 6 |
Journal | Physical Review Letters |
Volume | 119 |
Issue number | 14 |
Early online date | 4 Oct 2017 |
DOIs | |
Publication status | Published - 6 Oct 2017 |
Research Groups and Themes
- Engineering Mathematics Research Group
Fingerprint
Dive into the research topics of 'Localization Transition Induced by Learning in Random Searches'. Together they form a unique fingerprint.Profiles
-
Professor Luca Giuggioli
- School of Engineering Mathematics and Technology - Professor of Complexity Sciences
- Migration Mobilities Bristol
- Animal Behaviour and Sensory Biology
- Ecology and Environmental Change
Person: Academic , Member