ABSTRACT
For unperturbed and perturbed Kolmogorov models of population dynamics, new sufficient conditions of stability and boundedness with respect to two criteria (measures) are provided. An approach to treating Kolmogorov models of population dynamics via two measures was suggested. This approach worked out for both ordinary and partial differential equations allows conditions to obtain sufficient for the Kolmogorov models to possess various dynamical properties. This chapter continues the investigation in this direction and provides new stability and boundedness conditions for Kolmogorov-type ordinary differential equations. It introduces unperturbed and perturbed Kolmogorov models and takes multiplicative and additive perturbations into account. The chapter formulates boundedness and stability conditions with respect to two measures. It applies these conditions for the analysis of a generalized Lotka-Volterra model.
