Changing the Dynamic Modes in Populations with Short Life Cycle: Mathematical Modeling and Simulation
Frisman E.Ya., Neverova G.P., Kulakov M.P., Zhigalskii O.A.
Institute for Complex Analysis of Regional Problems of the Russian Academy of Sciences, Far Eastern branch (ICARP FEB RAS), Birobidzhan, Russia
Institute of Plant and Animal Ecology, Ural Division, Russian Academy of Sciences, Yekaterinburg, Russia
Abstract. It is revealed the phenomenon of multimode dynamics in a simple mathematical model describing the populations with short life cycle. This phenomenon consists in the existence of various dynamic modes under the same values of parameters, a transition to these modes determined by the initial conditions. This effect arises in the model that simultaneously possesses several different limit regimes: stable state, regular fluctuations, and chaotic attractor. The discovered phenomenon allows explaining both the occurrence of population number fluctuations and their disappearance. The adequacy of model dynamic modes is illustrated by their comparison to real population size dynamics of the bank vole (Myodes glareolus). The external climatic factor influence on reproduction processes in the population considerably expands a range of possible dynamic modes, and actually leads to a random walk into the attraction basins of these modes.
Key words: population dynamics, density-dependent regulation, mathematical modeling, multistability, bifurcations, attractor, basins of attraction.