Mathematical Model of Nicholson’s Experiment

Abstract

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.