Spatial pattern formation induced by Gaussian white noise

Mathematical Biosciences

Volumn 229, Issue 2, 2011, Pages 174-184

  Scarsoglio, Stefania ^a   Laio, Francesco ^a   D'Odorico, Paolo ^b   Ridolfi, Luca ^a  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF VIRGINIA   (United States)

Author keywords

Gaussian white noise; Noise induced phenomena; Spatial patterns

Indexed keywords

ANALYTICAL RESULTS; ANALYTICAL TOOL; DIFFUSION MECHANISMS; ENVIRONMENTAL DISTURBANCES; FIELD VARIABLES; GAUSSIAN NOISE; GAUSSIAN WHITE NOISE; LOCAL DYNAMICS; NOISE COMPONENTS; NOISE-INDUCED PHENOMENA; NUMERICAL SIMULATION; ORDERED STATE; SPATIAL COHERENCE; SPATIAL COUPLINGS; SPATIAL PATTERN FORMATION; SPATIAL PATTERNS; STRUCTURE-FUNCTION ANALYSIS;

DYNAMICAL SYSTEMS; DYNAMICS; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); LINEAR STABILITY ANALYSIS; MEAN FIELD THEORY;

WHITE NOISE;

ENVIRONMENTAL DISTURBANCE; GAUSSIAN METHOD; NUMERICAL MODEL; STOCHASTICITY; WHITE NOISE;

ARTICLE; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NORMAL DISTRIBUTION; STOCHASTIC MODEL; STRUCTURE ACTIVITY RELATION; WHITE NOISE;

ALGORITHMS; COMPUTER SIMULATION; ECOSYSTEM; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NATURE; STOCHASTIC PROCESSES;

EID: 79551566721     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.11.008     Document Type: Article

References (52)

1. Swift J., Hohenberg P.C. Hydrodynamics fluctuations at the convective instability. Phys. Rev. A 1977, 15:319.
2. Wu M.M., Ahlers G., Cannell D.S. Thermally-induced fluctuations below the onset of Rayleigh-Bénard convection. Phys. Rev. Lett. 1995, 75:1743.
3. Shuai J.W., Jung P. Optimal intracellular calcium signaling. Phys. Rev. Lett. 2002, 88.
4. Gluckman B.J., Netoff T.I., Neel E.J., Ditto W.L., Spano M.L., Schiff S.J. Stochastic resonance in a neuronal network from mammalian brain. Phys. Rev. Lett. 1996, 77:4098.
5. Macfadyen W.A. Soil and vegetation in British Somaliland. Nature 1950, 165:121.
6. Lefever R., Lejeune O. On the origin of tiger bush. Bull. Math. Biol. 1997, 59:263.
7. Klausmeier C.A. Regular and irregular patterns in semiarid vegetation. Science 1999, 284:1826.
8. Borgogno F., D'Odorico P., Laio F., Ridolfi L. Mathematical models of vegetation pattern formation in ecohydrology. Rev. Geophys. 2009, 47:RG1005.
9. Rodriguez-Iturbe I., Rinaldo A. Fractal River Basins: Chance and Self-Organization 2001, Cambridge University Press, Cambridge, UK.
10. S. Ikeda, G. Parker, River Meandering, Water Resources Monograph 12, American Geophysical Union, Washington, DC, 1989.
11. Allen J.R.L. Principles of physical sedimentology 1985, Cambridge University Press, Cambridge, UK.
12. Ashton A., Murray A.B., Arnoult O. Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature 2001, 414:296.
13. Bird E. Coastal Geomorphology, An Introduction 2000, John Wiley and Sons, Chichester.
14. Lancaster N. Geomorphology of Desert Dunes 1995, Routledge, London, New York.
15. White L.P. Vegetation stripes on sheet wash surfaces. J. Ecol. 1971, 59:615.
16. Montana C. The colonization of bare areas in 2-phase mosaics of an arid ecosystem. J. Ecol. 1992, 80:315.
17. Eddy J., Humphreys G.S., Hart D.M., Mitchell P.B., Fanning P.C. Vegetation arcs and litter dams: similarities and differences. Catena 1999, 37:57.
18. Bergkamp G., Cerda A., Imeson A.C. Magnitude-frequency analysis of water redistribution along a climate gradient in Spain. Catena 1999, 37:129.
19. Barbier N., Couteron P., Lejoly J., Deblauwe V., Lejeune O. Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns. J. Ecol. 2007, 94:537.
20. Ridolfi L., D'Odorico P., Laio F. Vegetation dynamics induced by phreatophyte-water table interactions. J. Theor. Biol. 2007, 248:301.
21. von Hardenberg J., Meron E., Shachak M., Zarmi Y. Diversity of vegetation patterns and desertification. Phys. Rev. Lett. 2001, 87:198101.
22. D'Odorico P., Laio F., Ridolfi L. Noise-induced stability in dryland plant ecosystems. Proc. Natl. Acad. Sci. USA 2005, 102:10819.
23. Turing A.M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London, Ser. B. 1952, 237:37.
24. Cross M.C., Hohenberg P.C. Pattern-formation outside of equilibrium. Rev. Mod. Phys. 1993, 65:851.
25. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability 1961, Clarendon, Oxford, UK.
26. Murray J.D. Mathematical Biology 2002, Springer, Berlin.
27. Manor A., Shnerb N.M. Origin of Pareto-like spatial distributions in ecosystems. Phys. Rev. Lett. 2008, 101:268104.
28. Couteron P., Lejeune O. Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model. J. Ecol. 2001, 89:616.
29. Rietkerk M., Van de Koppel J. Regular pattern formation in real ecosystems. Trends Ecol. Evol. 2008, 23:169.
30. Kefi S., Rietkerk M., Alados C.L., Pueyo Y., Papanastasis V.P., ElAich A., de Ruiter P.C. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 2007, 449:213.
31. Lefever R., Barbier N., Couteron P., Lejeune O. Deeply gapped vegetation patterns: On crown/root allometry, criticality and desertification. J. Theor. Biol. 2009, 261:194.
32. Sagues F., Sancho J.M., García-Ojalvo J. Spatio-temporal order out of noise. Rev. Mod. Phys. 2007, 79:829.
33. García-Ojalvo J., Sancho J.M. Noise in Spatially Extended Systems 1999, Springer-Verlag, New York.
34. Van den Broeck C., Parrondo J.M.R., Toral R. Noise-induced nonequilibrium phase transition. Phys. Rev. Lett. 1994, 73:3395.
35. van den Broeck C., Parrondo J.M.R., Toral R., Kawai R. Nonequilibrium phase transitions induced by multiplicative noise. Phys. Rev. E 1997, 55:4084.
36. Manor A., Shnerb N.M. Facilitation, competition, and vegetation patchiness: from scale free distribution to patterns. J. Theor. Biol. 2008, 253:838.
37. von Hardenberg J., Kletter A.Y., Yizhaq H., Nathan J., Meron E. Periodic versus scale-free patterns in dryland vegetation. Proc. R. Soc. B 2010, 277:1771.
38. Lejeune O., Tlidi M., Lefever R. Vegetation spots and stripes: dissipative structures in arid landscapes. Int. J. Quantum Chem. 2004, 98:261.
39. D'Odorico P., Caylor K., Okin G.S., Scanlon T.M. On soil moisture-vegetation feedbacks and their possible effects on the dynamics of dryland ecosystems. J. Geophys. Res. 2007, 112.
40. Zeng X.D., Shen S.S.P., Zeng X.B., Dickinson R.E. Multiple equilibrium states and the abrupt transitions in a dynamical system of soil water interacting with vegetation. Geophys. Res. Lett. 2004, 31.
41. Borgogno F., D'Odorico P., Laio F., Ridolfi L. Effect of rainfall interannual variability on the stability and resilience of dryland plant ecosystems. Water Resour. Res. 2007, 43.
42. Joffre R., Rambal S. How tree cover influences the water-balance of Mediterranean rangelands. Ecology 1993, 74:570.
43. Barbier N., Couteron P., Lejoly J., Deblauwe V., Lejeune O. Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems. J. Ecol. 2006, 94:537.
44. Rietkerk M., Dekker S.C., de Ruiter P.C., van de Koppel J. Self-organized patchiness and catastrophic shifts in ecosystems. Science 2004, 305:1926.
45. Becker A., Kramer L. Linear stability analysis for bifurcations in spatially extended systems with fluctuating control parameter. Phys. Rev. Lett. 1994, 73:7.
46. Parrondo J.M.R., van den Broeck C., Buceta J., DeLaRubia F.J. Noise-induced spatial patterns. Physica A 1996, 224:153.
47. Horsthemke W., Lefever R. Noise Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology 1984, Springer, Berlin.
48. Armero J., Sancho J.M., Casademunt J., Lacasta A.M., Ramirez Piscina L., Sagues F. External fluctuations in front propagation. Phys. Rev. Lett. 1996, 76:3045.
49. Panja D. Effects of fluctuations on propagating fronts. Phys. Rep. 2004, 393:87.
50. Buceta J., Lindenberg K. Spatial patterns induced by purely dichotomous disorder. Phys. Rev. E 2003, 68:011103.
51. Porporato A., D'Odorico P. Phase Transitions Driven by State-Dependent Poisson Noise. Phys. Rev. Lett. 2004, 92:110601.
52. Strikwerda J.C. Finite Difference Schemes and Partial Differential Equations 2004, SIAM, Philadelphia.