Influence of environmental noise on the dynamics of a realistic ecological model

Fluctuation and Noise Letters

Volumn 7, Issue 1, 2007, Pages

  Upadhyay, R K ^a   Mukhopadhyay, A ^b,d   Iyengar, S R K ^c,e  

^a INDIAN SCHOOL OF MINES   (India)

^b GVK BIOSCIENCES PVT LTD   (India)

^c INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^d TATA CONSULTANCY SERVICES   (India)

^e GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY   (India)

Author keywords

Chaotic dynamics; Environmental noise; Food Chain model

Indexed keywords

EID: 34147126277     PISSN: 02194775     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219477507003696     Document Type: Article

References (38)

1. K. M. Cuddington and P. Yodzis, Black noise and population persistence, Proc. R. Soc. Lond. B 266 (1999) 969-973.
2. J. B. Gao, S. K. Hwang and J. M. Liu, When can Noise Induce Chaos?, Physical review Letters 82(6) (1999) 1132-1135.
3. R. Lande, Risks of population extinction from demographic and environmental stochasticity and random catastrophes, Am. Nat., 142 (1993) 911-927.
4. R. M. May, Stability in randomly fluctuating deterministic environments, Am. Nat. 107 (1973) 621-650.
5. J. H. Steele, A comparison of terrestrial and marine ecological systems, Nature 313 (1985) 355-358.
6. J. M. G. Vilar and R. V. Sole Effect of noise in symmetric two-species competition, Physical Review Letters 80 (1998) 409-4102.
7. S.C. Warner, K.E. Limburg, A.H. Arino, M. Dodd, J. Dushoff, K.I. Sterfiou and J. Potts, Time series compared across the land-sea gradient In Ecological time series (eds. T.M. Powell and J.H. Steele), Chapman & Hall, New York, (1995) 242-273.
8. S. L. Pimm, The balance of Nature? Ecological issues in the conservation of species and communities. University of Chicago Press, Chicago (1991).
9. J. E. Cohen, Unexpected dominance of high frequencies in chaotic nonlinear populations models. Nature 378 (1995) 610-612.
10. J.H. Lawton, More time means more variation, Nature 334 (1988), 563.
11. R. M. May, Stability and Complexity in model ecosystems, Princeton University Press, Princeton, New Jersey (1974).
12. B. Dennis, R. Desharnais, A. Cushing and J. Costantino, Nonlinear demographic dynamics: mathematical models statistical methods and biological experiments, Ecol Monogr. 65 (1995) 261-281.
13. H. Tong, Nonlinear time series: a dynamical system approach, Oxford University Press, Oxford (1990).
14. J. Argyris, I. Andreadis, G. Pavlos and M. Athanasiou, The influence of noise on the correlation dimension of chaotic attractors, Chaos, Solitons and Fractals 9(3) (1998) 343-361.
15. S. Ellner and P. Turchin, Chaos in a noisy world: new methods and evidence from time series analysis, Am. Naturalist 145 (1995) 343-375.
16. D. Nychka, S. Ellner, D. McCaffrey and A. R. Gallant, Finding chaos in noisy systems, J. Roy Statist Soc B 54 (1992) 399-426.
17. R. M. May, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science 186 (1974) 645-647.
18. B. E. Kendall, Cycle, chaos, and noise in predator-prey dynamics, Chaos, Solitons and fractals 12 (2001) 321-332.
19. R.V. Sole, J. Valls and J. Bascompte , Spiral waves, chaos and multiple attractors in lattice models of interacting populations. Phys. Lett. A 166 (1992), 123-128.
20. R.K. Upadhyay and S. R. K. Iyengar, Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems, Nonlinear Analysis: real world applications 6 (2005) 509-530.
21. C-L Xu and Z-Z Li, Population dynamics and the color of environmental noise: A study on a three-species food-chain system, Ecological Research 18 (2003) 145-154.
22. J. Ripa, P. Lundberg and V. Kaitala, A general theory of environmental noise in ecological food webs, American Naturalist 107 (1998), 256-263.
23. B. Dennis, Allee effects in stochastic populations, Oikos, 96 (2002) 389-401.
24. M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978) 25-52.
25. R. M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976) 459-467.
26. R. M. May and G. F. Oster, Bifurcations and Dynamic Complexity in Simple Ecological Models, Am. Nat. 110 (1976) 573-599.
27. S. Parthasarathy and S. Sinha, Controlling Chaos in unidimensional maps using constant feedback, Phys. Rev. E 51 (1995) 6239-6242.
28. S. Gakkhar and K. N. Raid, Chaos in seasonally perturbed ratio-dependent prey-pradator system, Chaos Solitons and Fractals 15 (2003) 107-118.
29. S. Gakkhar and K. N. Raid, Seasonally perturbed prey-predator system with predator -dependent functional response, Chaos Solitons and Fractals 18 (2003) 1075-1083.
30. T. K. Kar, Influence of environmental noise on the Gompertz model of two species fishery, Ecological modeling 173 (2004) 283-293.
31. R. M. Nisbet and W. S. C. Gurney, Modelling Fluctuating population. Wiley Interscience, NY. (1982).
32. E. Renshaw, Modelling Biological population in space and time. Cambridge University Press, Cambridge (1991).
33. L. Arnold, Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, Inc. (1974).
34. G. Da. Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge (1992).
35. W.T. Coffey, Yu. P. Kalmykov and J.T. Waldron, The Langevin Equation with Applications in physics, Chemistry and Electrical Engineering. World Scientific (1997).
36. J. P. Crutchfield, J. D. Farmer and B. A. Huberman, Phys. Rep. 92 (1982) 46-50.
37. R. K. Upadhyay, V. Rai and S.R.K. Iyengar, Chaotic population dynamics and biology of top-predator, Chaos, Solitons and Fractals 21 (2004) 1195-1204.
38. V. Kaitala, J. Ylikarjula, E. Ranta and P. Lundberg, P. Population dynamics and the color of environmental noise.Proceedings of Royal society of London B 264 (1997) 943-948.