Survival of an evasive prey

Proceedings of the National Academy of Sciences of the United States of America

Volumn 106, Issue 33, 2009, Pages 13696-13701

  Oshanin, G ^a,b   Vasilyev, O ^c,d   Krapivskye, P L ^e   Klafter, J ^f,g  

^a INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^d UNIVERSITY OF STUTTGART   (Germany)

^e Boston University   (United States)

^f TEL AVIV UNIVERSITY   (Israel)

^g UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Chase; Diffusion; First passage times; Pursuit; Superdiffusion

Indexed keywords

ARTICLE; DIFFUSION COEFFICIENT; MATHEMATICAL MODEL; PREDATOR; PREDATOR AVOIDANCE; PREDATOR PREY INTERACTION; PREY; PRIORITY JOURNAL; SURVIVAL RATE;

ALGORITHMS; ANIMALS; BEHAVIOR, ANIMAL; BODY SIZE; ECOSYSTEM; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; MOVEMENT; POPULATION DENSITY; PREDATORY BEHAVIOR;

EID: 69549111585     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.0904354106     Document Type: Article

References (28)

1. Nahin P (2007) Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton Univ Press, Princeton).
2. Weihs D, Webb PW (1984) Optimal avoidance and evasion tactics in predator-prey interactions. J Theor Biol 106:189-206.
3. Miller GF, Cliff D (1994) Co-evolution of pursuit and evasion: Biological and game-theoretical foundations. Technical Report CSRP311 (University of Sussex, Brighton, UK).
4. Krapivsky PL, Redner S (1996) Kinetics of a diffusive capture process: Lamb besieged by a pride of lions. J Phys A 29:5347-5357. (Pubitemid 126689332)
5. Redner S, Krapivsky P L (1999) Capture of the lamb: Diffusing predators seeking a diffusing prey. Amer J Phys 67:1277-1283.
6. Isaacs R (1965) Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (Wiley, New York).
7. Bray AJ, Majumdar SN, Blythe R (2003) A formal solution of a class of reaction-diffusion models: Reduction to a single-particle problem. Phys Rev E 67:060102.
8. Moreau M, Oshanin G, Bénichou O, Coppey M (2003) Pascal principle for diffusion-controlled trapping reactions. Phys Rev E 67:045104.
9. Moreau M, Oshanin G, Bénichou O, Coppey M (2004) Lattice theory of trapping reactions with mobile species. Phys Rev E 69:046101.
10. Tachiya M (1983) Theory of diffusion-controlled reactions: Formulation of the bulk reaction rate in terms of the pair probability. Radiat Phys Chem 21:167-175.
11. Blumen A, Zumofen G, Klafter J (1984) Target annihilation by random walkers. Phys Rev B 30:5379-5382.
12. Redner S, Kang K (1984) Kinetics of the 'scavenger' reaction. J Phys A 17:L451-L455.
13. Dvoretzky A, Erdös P (1951) Some problems on random walks in space. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, ed Neyman J, (Univ California Press, Berkeley) pp 353-367.
14. Brummelhuis MJAM, Hilhorst HJ (1991) Covering of a finite lattice by a random walk. Physica A 176:387-408.
15. Bénichou O, Moreau M, Oshanin G (2000) Kinetics of stochastically gated diffusion-limited reactions and geometry of random walk trajectories. Phys Rev E 61:3388-3406.
16. Weiss GH, Havlin S, Bunde A (1985) On the survival probability of a random walk in a finite lattice with a single trap. J Stat Phys 40:1572-9613.
17. Grigoriev IV, Makhnovskii YA, Bereshkovskii AM, Zitserman VY (2002) Kinetics of escape through a small hole. J Chem Phys 116:9574-9577.
18. Schuss Z, Singer A, Holcman D (2007) The narrow escape problem for diffusion in cellular microdomains. Proc Natl Acad Sci USA 104:16098-16103. (Pubitemid 350103425)
19. Bénichou O, Voituriez R (2008) Narrow-escape time problem: Time needed for a particle to exit a confining domain through a small window. Phys Rev Lett 100:168105. (Pubitemid 351585520)
20. Weiss GH, Shuler KE, Lindenberg K (1983) Order statistics for first passage times in diffusion processes. J Stat Phys 31:255-278.
21. Bogunà M, Berezhkovskii AM, Weiss GH (2000) Occupancy of a single site by many random walkers. Phys Rev E 62:3250-3256. (Pubitemid 30938838)
22. Bénichou O, Coppey M, Klafter J, Moreau M, Oshanin G (2003) On the joint residence time of N independent two-dimensional Brownian motions. J Phys A 36:7225-7231. (Pubitemid 37347053)
23. Stefani FD, Hoogenboom JP, Barkai E (2009) Beyond quantum jumps: Blinking nanoscale light emitters. Phys Today 62(2):34-39.
24. Bray AJ, Blythe R (2002) A exact asymptotics for one-dimensional diffusion with mobile traps. Phys Rev Lett 89:150601.
25. Blythe R A, Bray A J (2003) Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps. Phys Rev E 67:041101.
26. Oshanin G, Bénichou O, Coppey M, Moreau M (2002) Trapping reactions with randomly moving traps: Exact asymptotic results for compact exploration. Phys Rev E 66:060101.
27. Yuste S B, Oshanin G, Lindenberg K, Bénichou O, Klafter J (2008) Survival probability of a particle in a sea of mobile traps: A tale of tails. Phys Rev E 78:021105.
28. Sanders DP, Larralde H (2008) How rare are diffusive rare events? Europhys Lett 82:40005-40011.