Population dynamics advected by chaotic flows: A discrete-time map approach

Chaos

Volumn 11, Issue 2, 2001, Pages 397-403

  López, Cristóbal ^a,b   Hernández García, Emilio ^a   Piro, Oreste ^a   Vulpiani, Angelo ^b,c   Zambianchi, Enrico ^d  

^a INSTITUTO MEDITERRÁNEO DE ESTUDIOS AVANZADOS   (Spain)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^c INFM   (Italy)

^d Istituto Universitario Navale   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035374326     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1371285     Document Type: Article

References (25)

1. E. R. Abraham, "The generation of plankton patchiness by turbulent stirring," Nature (London) 391, 577 (1998).
2. M. J. R. Fasham. "The statistical and mathematical analysis of plankton patchiness," Oceanogr. Mar. Biol. 16, 43 (1978).
3. J. H. Steele, Spatial Patterns in Plankton Communities (Plenum, New York, 1978).
4. J. H. Steele and E. W. Henderson, "Coupling between physical and biological scales," Philos. Trans. R. Soc. London, Ser. B 343, 5 (1994).
5. L. Mazzella, M. C. Buia, M. C. Gambi, M. Lorenti, G. F. Russo, M. B. Scipione, and V. Zupo, "Plant-animal trohic relationships in the Posidonia Oceanica ecosystem of the Mediterranean Sea: A review," in Plant-Animal Interactions in the Marine Benthos, edited by D. M. John, S. J. Hawkins, and J. H. Price (Clarendon, Oxford, 1992), p. 165.
6. I. R. Jenkinson and B. A. Biddanda, "Bulk-phase viscoelastic properties of seawater: Relationship with plankton components," J. Plankton Res. 17, 2251 (1995).
7. I. R. Jenkinson, T. Wyatt, and A. Malej, "How viscoelastic effects of colloidal biopolymers modify rheological properties of seawater," in Progress and Trends in Rheology 5, edited by I. Emri and R. Cvelbar (Springer-Verlag, New York, 1998), p. 57.
8. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989).
9. J. H. E. Cartwright, M. Feingold, and O. Piro, "An introduction to chaotic advection," in Mixing: Chaos and Turbulence, edited by H. Chaté, E. Villermaux, and J.-M. Chomaz (Kluwer Academic/Plenum, New York, 1999).
10. J. H. E. Cartwright, M. Feingold, and O. Piro, "Passive scalars and three-dimensional Liouvillian maps," Physica D 76, 22 (1994).
11. T. Tél, G. Károlyi, A. Péntek, I. Scheuring, Z. Toroczkai, C. Grebogi, and J. Kadtke, "Chaotic advection, diffusion, and reactions in open flows," Chaos 10, 89 (2000).
12. M. A Bees, I. Mezic, and J. McGlade, "Planktonic interactions and chaotic advection in Langmuir circulation," Math. Comput. Simul. 44, 527 (1998); Z. Toroczkai, G. Károlyi, A. Péntek, T. Tél, and C. Grebogi, "Advection of active particles in open chaotic flows," Phys. Rev. Lett. 80, 500 (1998); A. Péntek, T. Károlyi, I. Scheuring, T. Tél, Z. Toroczkai, J. Kadtke, and C. Grebogi, "Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows," Physica A 274, 120 (1999).
13. M. A Bees, I. Mezic, and J. McGlade, "Planktonic interactions and chaotic advection in Langmuir circulation," Math. Comput. Simul. 44, 527 (1998); Z. Toroczkai, G. Károlyi, A. Péntek, T. Tél, and C. Grebogi, "Advection of active particles in open chaotic flows," Phys. Rev. Lett. 80, 500 (1998); A. Péntek, T. Károlyi, I. Scheuring, T. Tél, Z. Toroczkai, J. Kadtke, and C. Grebogi, "Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows," Physica A 274, 120 (1999).
14. M. A Bees, I. Mezic, and J. McGlade, "Planktonic interactions and chaotic advection in Langmuir circulation," Math. Comput. Simul. 44, 527 (1998); Z. Toroczkai, G. Károlyi, A. Péntek, T. Tél, and C. Grebogi, "Advection of active particles in open chaotic flows," Phys. Rev. Lett. 80, 500 (1998); A. Péntek, T. Károlyi, I. Scheuring, T. Tél, Z. Toroczkai, J. Kadtke, and C. Grebogi, "Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows," Physica A 274, 120 (1999).
15. Z. Neufeld, C. López, and P. H. Haynes, "Smooth-filamental transition of active tracer fields stirred by chaotic advection." Phys. Rev. Lett. 82, 2606 (1999).
16. Z. Neufeld, C. López, E. Hernández-García, and T. Tél, "The multifractal structure of chaotically advected chemical fields," Phys. Rev. E 61, 3857 (2000).
17. I. Scheuring, G. Károlyi, A. Péntek. T. Tél. and Z. Toroczkai, "A model for resolving the plankton paradox: Coexistence in open flows," Freshwater Biol. 45, 123 (2000); C. López, Z. Neufeld, E. Hernández-García, and P. H. Haynes, "Chaotic advection of reacting substances: Plankton dynamics on a meandering jet," Phys. Chem. Earth B 26, 313 (2001).
18. I. Scheuring, G. Károlyi, A. Péntek. T. Tél. and Z. Toroczkai, "A model for resolving the plankton paradox: Coexistence in open flows," Freshwater Biol. 45, 123 (2000); C. López, Z. Neufeld, E. Hernández-García, and P. H. Haynes, "Chaotic advection of reacting substances: Plankton dynamics on a meandering jet," Phys. Chem. Earth B 26, 313 (2001).
19. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer-Verlag, New York, 1992).
20. V. Loreto, G. Paladin, M. Pasquini, and A. Vulpiani, "Characterization of chaos in random maps," Physica A 232, 189 (1996).
21. C.-H. Lai and C. Zhou, "Synchronization of chaotic maps by symmetric common noise," Europhys. Lett. 43, 376 (1998).
22. R. Toral, C. R. Mirasso, E. Hernández-García, and O. Piro, Synchronization of Chaotic Systems by Common Random Forcing in Unsolved Problems of Noise and Fluctuations: UPON'99, Second International Conference, edited by D. Abbot and L. Kish (AIP, Melville, 2000); "Analytical and numerical studies of noise-induced synchronization of chaotic systems," preprint nlin.CD/0104044.
23. R. Toral, C. R. Mirasso, E. Hernández-García, and O. Piro, Synchronization of Chaotic Systems by Common Random Forcing in Unsolved Problems of Noise and Fluctuations: UPON'99, Second International Conference, edited by D. Abbot and L. Kish (AIP, Melville, 2000); "Analytical and numerical studies of noise-induced synchronization of chaotic systems," preprint nlin.CD/0104044.
24. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, New York, 1988).
25. R| also indicates that the stirring due to the flow is very strong. That is, we consider the case of fast stirring time-scales, in which slow activity is accompanied by vigorous mixing.