Spatial dynamics in a predator-prey model with herd behavior

Chaos

Volumn 23, Issue 3, 2013, Pages

  Yuan, Sanling ^a   Xu, Chaoqun ^a   Zhang, Tonghua ^b  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

^b SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; COMPUTER SIMULATION; ECOLOGY; ECOSYSTEM; POPULATION DENSITY; POPULATION GROWTH; PREDATION; THEORETICAL MODEL;

ANIMALS; COMPUTER SIMULATION; ECOLOGY; ECOSYSTEM; MODELS, THEORETICAL; POPULATION DENSITY; POPULATION GROWTH; PREDATORY BEHAVIOR;

EID: 84884929111     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4812724     Document Type: Article

References (54)

1. Freedman H.I. Deterministic Mathematical Models in Population Ecology 1980, (Marcel Dekker, New York).
2. Baurmanna M. Gross T. Feudel U. J. Theor. Biol. 2007, 245:220. 10.1016/j.jtbi.2006.09.036
3. Holling C.S. Can. Entomol. 1959, 91:293. 10.4039/Ent91293-5.
4. Holling C.S. Can. Entomol. 1959, 91:385. 10.4039/Ent91385-7.
5. Hassell M.P. Varley G.C. Nature 1969, 223:1133. 10.1038/2231133a0
6. Beddington J.R. J. Animal Ecol. 1975, 44:331. 10.2307/3866.
7. DeAngelis D.L. Goldsten R.A. O'Neill R.V. Ecology 1975, 56:881. 10.2307/1936298
8. Crowley P.H. Martin E.K. J. North Am. Benthol. Soc. 1989, 8:211. 10.2307/1467324
9. Berryman A.A. Ecology 1992, 73:1530. 10.2307/1940005.
10. Kuang Y. Beretta E. J. Math. Biol. 1998, 36:389. 10.1007/s002850050105
11. Zhang X.-A. Chen L.-S. Neumann A.U. Math. Biosci. 2000, 168:201. 10.1016/S0025-5564(00)00033-X
12. Aziz-Alaoui M.A. Okiye M.D. Appl. Math. Lett. 2003, 16:1069. 10.1016/S0893-9659(03)90096-6
13. Nindjin A.F. Aziz-Alaoui M.A. Cadivel M. Nonlinear Anal. RWA 2006, 7:1104. 10.1016/j.nonrwa.2005.10.003
14. Han L.-T. Ma Z.-E. Hethcote H.W. Math. Comput. Model. 2001, 34:849. 10.1016/S0895-7177(01)00104-2
15. Xu R. Ma Z.-E. Nonlinear Anal. RWA 2008, 9:1444. 10.1016/j.nonrwa.2007.03.015
16. Liu M. Wang K. Commun. Nonlinear Sci. Numer. Simul. 2011, 16:3792. 10.1016/j.cnsns.2010.12.026
17. Ji C.-Y. Jiang D.-Q. Li X.-Y. J. Comput. Appl. Math. 2011, 235:1326. 10.1016/j.cam.2010.08.021
18. Ajraldi V. Pittavino M. Venturino E. Nonlinear Anal. RWA 2011, 12:2319. 10.1016/j.nonrwa.2011.02.002
19. Braza P.A. Nonlinear Anal. RWA 2012, 13:1837. 10.1016/j.nonrwa.2011.12.014.
20. Brentnall S.J. Richards K.J. Brindley J. Murphy E. J. Plankton Res. 2003, 25:121. 10.1093/plankt/25.2.121
21. Fulton E.A. Smith A.D. M. Johnson C.R. Ecol. Modell. 2003, 169:157. 10.1016/S0304-3800(03)00268-0
22. Segel L.A. Jackson J.L. J. Theor. Biol. 1972, 37:545. 10.1016/0022-5193(72)90090-2
23. Mimura M. Murray J.D. J. Theor. Biol. 1978, 75:249. 10.1016/0022-5193(78)90332-6
24. Okubo A. Levin L.A. Diffusion and Ecological Problems: Modern Perspective, Interdisciplinary Applied Mathematics 2001, and 2nd ed. (Springer, New York).
25. Murray J.D. J. Theor. Biol. 1981, 88:161. 10.1016/0022-5193(81)90334-9.
26. Bascompte J. Solé R.V. Martínez N. J. Theor. Biol. 1997, 187:213. 10.1006/jtbi.1997.0430
27. Bascompte J. Solé R.V. Trends Ecol. Evol. 1998, 13:173. 10.1016/S0169-5347(98)01325-1
28. Sun G.-Q. Zhang G. Jin Z. Li L. Nonlinear Dynam. 2009, 58:75. 10.1007/s11071-008-9462-z
29. Wang W.-M. Liu Q.-X. Jin Z. Phys. Rev. E 2007, 75:051913. 10.1103/PhysRevE.75.051913
30. Zhang X.-C. Sun G.-Q. Jin Z. Phys. Rev. E 2012, 85:021924. 10.1103/PhysRevE.85.021924
31. Guan X.-N. Wang W.-M. Cai Y.-L. Nonlinear Anal. RWA 2011, 12:2385. 10.1016/j.nonrwa.2011.02.011
32. Rodrigues T. Tomé T. Braz. J. Phys. 2008, 38:87
33. Argolo C. Otaviano H. Gleria I. Arashiro E. Tomé T. Int. J. Bifurcation Chaos 2010, 20:309. 10.1142/S0218127410025752
34. Kraenkel R.A. Pamplona da Silva D.J. Physica A 2010, 389:60. 10.1016/j.physa.2009.09.023
35. Pamplona da Silva D.J. Kraenkel R.A. Physica A 2012, 391:142. 10.1016/j.physa.2011.08.029
36. Azevedo F. Kraenkel R.A. Pamplona da Silva D.J. Ecol. Complex. 2012, 11:154. 10.1016/j.ecocom.2012.06.001
37. Turing A.M. B. Math. Biol. 1990, 52:153.
38. Ouyang Q. Swinney H.L. Nature 1991, 352:610. 10.1038/352610a0
39. Dufiet V. Boissonade J. Phys. Rev. E 1996, 53:4883. 10.1103/PhysRevE.53.4883
40. Varea C. Aragón J.L. Barrio R.A. Phys. Rev. E 1997, 56:1250. 10.1103/PhysRevE.56.1250
41. Kondo S. Asai R. Nature 1995, 376:765. 10.1038/376765a0
42. Saunoriene L. Ragulskis M. Phys. Rev. E 2011, 84:056213. 10.1103/PhysRevE.84.056213
43. Biktashev V.N. Tsyganov M.A. Phys. Rev. Lett. 2011, 107:134101. 10.1103/PhysRevLett.107.134101
44. Peña B. Pérez-García C. Phys. Rev. E 2001, 64:056213. 10.1103/PhysRevE.64.056213
45. Ouyang Q. Nonlinear Science and the Pattern Dynamics Introduction 2010, (Peking University Press, Beijing).
46. Cross M.C. Hohenberg P.C. Rev. Mod. Phys. 1993, 65:851. 10.1103/RevModPhys.65.851
47. Sun G.-Q. Jin Z. Liu Q.-X. Li L. J. Stat. Mech. 2007, 2007:P11011. 10.1088/1742-5468/2007/11/P11011
48. Ipsen M. Hynne F. Sorensen P.G. Physica D 2000, 136:66. 10.1016/S0167-2789(99)00149-9
49. Wang W.-M. Wang W.-J. Li Y.-Z. Tan Y.-J. Chin. Phys. B 2011, 20:034702. 10.1088/1674-1056/20/3/034702
50. Wang W.-M. Li Y.-Z. Rao F. Zhang L. Tan Y.-J. J. Stat. Mech. 2010, 2010:P11036. 10.1088/1742-5468/2010/11/P11036
51. Sun G.-Q. Jin Z. Liu Q.-X. Li L. Chin. Phys. B 2008, 17:3936. 10.1088/1674-1056/17/11/003
52. Zhang J.-F. Li W.-T. Yan X.-P. Appl. Math. Comput. 2011, 218:1883. 10.1016/j.amc.2011.06.071
53. Ciliberto S. Coullet P. Lega J. Pampaloni E. Perez-Garcia C. Phys. Rev. Lett. 1990, 65:2370. 10.1103/PhysRevLett.65.2370
54. Sun G.-Q. Jin Z. Liu Q.-X. Li B.-L. BioSystem 2010, 100:14. 10.1016/j.biosystems.2009.12.003