1 research outputs found
Identification of nonlinear noisy dynamics of an ecosystem from observations of one of its trajectory components
The problem of determining dynamical models and trajectories that describe
observed time-series data allowing for the understanding, prediction and
possibly control of complex systems in nature is of a great interest in a wide
variety of fields. Often, however, only part of the system's dynamical
variables can be measured, the measurements are corrupted by noise and the
dynamics is complicated by an interplay of nonlinearity and random
perturbations. The problem of dynamical inference in these general settings is
challenging researchers for decades. We solve this problem by applying a
path-integral approach to fluctuational dynamics, and show that, given the
measurements, the system trajectory can be obtained from the solution of the
certain auxiliary Hamiltonian problem in which measured data act effectively as
a control force driving the estimated trajectory toward the most probable one
that provides a minimum to certain mechanical action. The dependance of the
minimum action on the model parameters determines the statistical distribution
in the model space consistent with the measurements. We illustrate the
efficiency of the approach by solving an intensively studied problem from the
population dynamics of predator-prey system where the prey populations may be
observed while the predator populations or even their number is difficult or
impossible to estimate. We apply our approach to recover both the unknown
dynamics of predators and model parameters (including parameters that are
traditionally very difficult to estimate) directly from measurements of the
prey dynamics. We provide a comparison of our method with the Markov Chain
Monte Carlo technique.Comment: 30 pages, 7 figure