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The paper proposes a mathematical model that describes mouse-like rodent population dynamics. The model is examined through analytical and numerical methods. Changes in the population parameter values lead to a complex evolution of dynamic regimes observed, namely periodic, quasi-periodic and chaotic oscillations, as well as changes in dynamic regimes caused by multistability and external factors. Multistability consists in the existence of various dynamic regimes under the same values of parameters; a transition to these regimes is determined by the initial conditions. An approach is proposed to study multistability by analysing annual population surveys and the model parameter estimates corresponding to the real data set, as well as environmental factors that influence both the birth rate and self-regulation. The adequacy of the results obtained is illustrated by comparing the simulations with the real dynamics of the bank vole population (Myodes glareolus) as a typical example of mouse-like rodents under non-constant environmental conditions. The model study shows that external factors lead to a significant change in attraction basins of coexisting dynamic regimes and shift in model parameter values over the parametric space, which results in a trajectory transition from one dynamic regime to another. As a result, the population size shifts between attraction basins of different dynamic regimes. In certain years, the population size can be attracted to an area of parameter values with similar regimes (the same period of cycles). In particular, the real dynamics of the bank vole population can be represented by a sequence of alternating transients that lead to fluctuations with 3-, 6-, 7- or 14-year periods under constant climatic conditions.