Mathematical Model of Nicholson’s Experiment
Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A p...
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Yaroslavl State University
2017-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/525 |
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| author | Sergey D. Glyzin |
| author_facet | Sergey D. Glyzin |
| author_sort | Sergey D. Glyzin |
| collection | DOAJ |
| description | Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations. |
| format | Article |
| id | doaj-art-078976950a9f466dbdf0d0e1a15aa515 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2017-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-078976950a9f466dbdf0d0e1a15aa5152025-08-20T03:44:17ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-06-0124336538610.18255/1818-1015-2017-3-365-386375Mathematical Model of Nicholson’s ExperimentSergey D. Glyzin0P.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASConsidered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.https://www.mais-journal.ru/jour/article/view/525differential-difference equationsasymptotic behaviourstabilitylyapunov exponentsinsect population dynamics |
| spellingShingle | Sergey D. Glyzin Mathematical Model of Nicholson’s Experiment Моделирование и анализ информационных систем differential-difference equations asymptotic behaviour stability lyapunov exponents insect population dynamics |
| title | Mathematical Model of Nicholson’s Experiment |
| title_full | Mathematical Model of Nicholson’s Experiment |
| title_fullStr | Mathematical Model of Nicholson’s Experiment |
| title_full_unstemmed | Mathematical Model of Nicholson’s Experiment |
| title_short | Mathematical Model of Nicholson’s Experiment |
| title_sort | mathematical model of nicholson s experiment |
| topic | differential-difference equations asymptotic behaviour stability lyapunov exponents insect population dynamics |
| url | https://www.mais-journal.ru/jour/article/view/525 |
| work_keys_str_mv | AT sergeydglyzin mathematicalmodelofnicholsonsexperiment |