Sustained oscillations in stochastic systems
Many non-linear deterministic models for interacting populations present damped oscillations towards the corresponding equilibrium values. However, simulations produced with related stochastic models usually present sustained oscillations which preserve the natural frequency of the damped oscillatio...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2001
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 05931caa a22007217a 4500 | ||
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| 001 | PAPER-2089 | ||
| 003 | AR-BaUEN | ||
| 005 | 20240930113353.0 | ||
| 008 | 190411s2001 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0035135563 | |
| 030 | |a MABIA | ||
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Aparicio, Juan Pablo | |
| 245 | 1 | 0 | |a Sustained oscillations in stochastic systems |
| 260 | |c 2001 | ||
| 270 | 1 | 0 | |m Aparicio, J.P.; Department of Biometrics, Cornell University, 432 Warren Hall, Ithaca, NY 14853-7801, United States; email: jpa9@cornell.edu |
| 504 | |a Renshaw, E., (1991) Modelling Biological Populations in Space and Time, , Cambridge University, Cambridge | ||
| 504 | |a Nåsell, I., On the time to extinction in recurrent epidemics (1999) J. Roy. Statist. Soc. B, 61, p. 309 | ||
| 504 | |a Murray, J.D., (1989) Mathematical Biology, , Springer, Heidelberg | ||
| 504 | |a Siegman, A.E., (1986) Lasers, , University Science Books, Mill Valley | ||
| 504 | |a Soper, H.E., Interpretation of periodicity in disease prevalence (1929) J. Roy. Statist. Soc. A, 92, p. 34 | ||
| 504 | |a Bartlett, M.S., Measles periodicity and community size (1957) J. Roy. Statist. Soc. A, 120, p. 48 | ||
| 504 | |a Bartlett, M.S., The critical community size for measles in the United States (1960) J. Roy. Statist. Soc. A, 123, p. 37 | ||
| 504 | |a Grenfell, B.T., Bolker, B., Kleczkowski, A., Seasonality, demography and the dynamics of measles in developed countries (1995), p. 248. , D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University, Cambridge; Keeling, M.J., Grenfell, B.T., Disease extinction and community size: Modeling the persistence of measles (1997) Science, 275, p. 65 | ||
| 504 | |a Van Herwaarden, O.A., Grasman, J., Stochastic epidemics: Major outbreaks and the duration of the endemic period (1995) J. Math. Biol., 33, p. 581 | ||
| 504 | |a Van Kampen, N.G., (1981) Stochastic Processes in Physics and Chemistry, , North-Holland, Amsterdam | ||
| 504 | |a Solari, H.G., Natiello, M.A., Mindlin, B.G., (1996) Non-linear Dynamics: A Two-way Trip from Physics to Math, , Institute of Physics, Bristol | ||
| 504 | |a Guckenheimer, J., Holmes, P.J., (1986) Non-linear Oscillators, Dynamical Systems and Bifurcations of Vector Fields, , Springer, New York, (first printing: 1983.) | ||
| 504 | |a Kushner, H.J., (1967) Stochastic Optimization and Control, pp. 47-57. , Wiley, New York, (Chapter: The concept of invariant set for stochastic dynamical systems and applications to stochastic stability) | ||
| 504 | |a Kushner, H.J., Stability of Stochastic Dynamical Systems (1968), 294, pp. 97-124. , Lecture Notes in Mathematics, Springer, Berlin, (Chapter: Stochastic stability); Meyn, S.P., Tweedie, R.L., (1993) Markov Chains and Stochastic Stability, , Springer, London | ||
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a Many non-linear deterministic models for interacting populations present damped oscillations towards the corresponding equilibrium values. However, simulations produced with related stochastic models usually present sustained oscillations which preserve the natural frequency of the damped oscillations of the deterministic model but showing non-vanishing amplitudes. The relation between the amplitude of the stochastic oscillations and the values of the equilibrium populations is not intuitive in general but scales with the square root of the populations when the ratio between different populations is kept fixed. In this work, we explain such phenomena for the case of a general epidemic model. We estimate the stochastic fluctuations of the populations around the equilibrium point in the epidemiological model showing their (approximated) relation with the mean values. © 2001 Elsevier Science Inc. |l eng | |
| 536 | |a Detalles de la financiación: Universidad de Buenos Aires, TW04 | ||
| 536 | |a Detalles de la financiación: It is a pleasure to acknowledge valuable discussions with B. Gabriel Mindlin, Mario A. Natiello and Ingemar Nåsell. We acknowledge support from the Universidad de Buenos Aires, grant TW04. J.P.A. acknowledges support from the Mathematical and Theoretical Biology Institute at Cornell University. | ||
| 593 | |a Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 593 | |a Department of Biometrics, 432 Warren Hall, Cornell University, Ithaca, NY 14853-7801, United States | ||
| 690 | 1 | 0 | |a INTERACTING POPULATIONS |
| 690 | 1 | 0 | |a NON-LINEAR DYNAMICS |
| 690 | 1 | 0 | |a POPULATION DYNAMICS |
| 690 | 1 | 0 | |a STOCHASTIC OSCILLATIONS |
| 690 | 1 | 0 | |a OSCILLATION |
| 690 | 1 | 0 | |a POPULATION MODELING |
| 690 | 1 | 0 | |a STOCHASTICITY |
| 690 | 1 | 0 | |a ARTICLE |
| 690 | 1 | 0 | |a EPIDEMIC |
| 690 | 1 | 0 | |a HUMAN |
| 690 | 1 | 0 | |a MATHEMATICAL MODEL |
| 690 | 1 | 0 | |a NONLINEAR SYSTEM |
| 690 | 1 | 0 | |a OSCILLATION |
| 690 | 1 | 0 | |a POPULATION DYNAMICS |
| 690 | 1 | 0 | |a STOCHASTIC MODEL |
| 690 | 1 | 0 | |a MODELS, BIOLOGICAL |
| 690 | 1 | 0 | |a POPULATION DYNAMICS |
| 690 | 1 | 0 | |a STOCHASTIC PROCESSES |
| 700 | 1 | |a Solari, H.G. | |
| 773 | 0 | |d 2001 |g v. 169 |h pp. 15-25 |k n. 1 |p Math. Biosci. |x 00255564 |w (AR-BaUEN)CENRE-6039 |t Mathematical Biosciences | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035135563&doi=10.1016%2fS0025-5564%2800%2900050-X&partnerID=40&md5=67b91c37260b624f99682ac4dacc07fe |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1016/S0025-5564(00)00050-X |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00255564_v169_n1_p15_Aparicio |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255564_v169_n1_p15_Aparicio |y Registro en la Biblioteca Digital |
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| 999 | |c 63042 | ||