en
2017-12
true
https://scigraph.springernature.com/explorer/license/
2019-04-10T21:54
articles
research_article
2017-12-01
Considered is a mathematical model of insects population dynamics and an attempt is made to explain classical experimental results of Nicholson based on it. 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 stability loss of the equilibrium of the problem leads to the bifurcation of stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain classical Nicholson’s experiment, which detailed theoretical rationale is given in the last section. There for an attractor of the system the largest Lyapunov exponent is computed. The nature of change of this exponent allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to combination of analytical and numerical methods in studying of 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.
736-752
Mathematical Model of Nicholson’s Experiment
http://link.springer.com/10.3103/S0146411617070331
S. D.
Glyzin
Demidov Yaroslavl State University, 150003, Yaroslavl, Russia
Scientific Center in Chernogolovka RAS, 142432, Chernogolovka, Moscow oblast, Russia
Scientific Center
Springer Nature - SN SciGraph project
Mathematical Sciences
51
doi
10.3103/s0146411617070331
d341cc63f5015d9a403d6ae58cdbcbbfc6a3813eca62c866ee2e55b041a72829
readcube_id
0146-4116
Automatic Control and Computer Sciences
1558-108X
Applied Mathematics
dimensions_id
pub.1101073966
7