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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todo:paper_00255564_v169_n1_p15_Aparicio2023-10-03T14:36:06Z Sustained oscillations in stochastic systems Aparicio, J.P. Solari, H.G. Interacting populations Non-linear dynamics Population dynamics Stochastic oscillations oscillation population modeling stochasticity article epidemic human mathematical model nonlinear system oscillation population dynamics stochastic model Models, Biological Population Dynamics Stochastic Processes 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. Fil:Aparicio, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255564_v169_n1_p15_Aparicio |
| institution |
Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Interacting populations Non-linear dynamics Population dynamics Stochastic oscillations oscillation population modeling stochasticity article epidemic human mathematical model nonlinear system oscillation population dynamics stochastic model Models, Biological Population Dynamics Stochastic Processes |
| spellingShingle |
Interacting populations Non-linear dynamics Population dynamics Stochastic oscillations oscillation population modeling stochasticity article epidemic human mathematical model nonlinear system oscillation population dynamics stochastic model Models, Biological Population Dynamics Stochastic Processes Aparicio, J.P. Solari, H.G. Sustained oscillations in stochastic systems |
| topic_facet |
Interacting populations Non-linear dynamics Population dynamics Stochastic oscillations oscillation population modeling stochasticity article epidemic human mathematical model nonlinear system oscillation population dynamics stochastic model Models, Biological Population Dynamics Stochastic Processes |
| description |
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. |
| format |
JOUR |
| author |
Aparicio, J.P. Solari, H.G. |
| author_facet |
Aparicio, J.P. Solari, H.G. |
| author_sort |
Aparicio, J.P. |
| title |
Sustained oscillations in stochastic systems |
| title_short |
Sustained oscillations in stochastic systems |
| title_full |
Sustained oscillations in stochastic systems |
| title_fullStr |
Sustained oscillations in stochastic systems |
| title_full_unstemmed |
Sustained oscillations in stochastic systems |
| title_sort |
sustained oscillations in stochastic systems |
| url |
http://hdl.handle.net/20.500.12110/paper_00255564_v169_n1_p15_Aparicio |
| work_keys_str_mv |
AT apariciojp sustainedoscillationsinstochasticsystems AT solarihg sustainedoscillationsinstochasticsystems |
| _version_ |
1807319570885640192 |