Galina Neverova

The paper studies dynamic modes of the Ricker model with the periodic Malthusian parameter. The equation parametric space is shown to have multistability areas in which different dynamic modes are possible depending on the initial conditions. In particular, the model trajectory can asymptotically tend either to a stable cycle or to a chaotic attractor. Oscillation synchronization of the 2-cycles and the Malthusian parameter of the model are studied. Fluctuations in population size and environmental factors can be either synchronous or asynchronous. The structural features of attraction basins in phase space are investigated for possible stable dynamic modes.

This paper is concerned with the model of dynamics for population with a simple age structure. It is assumed that the growth of population size is regulated by limiting the survival rate of younger individuals. It is shown that the density-dependent regulation of offspring survival can lead to fluctuations in population size. Moreover, there are multistability areas in which the type of dynamic regimes depends on the initial conditions. These aspects of dynamic behavior can explain the changes in the oscillation period, and the appearance and disappearance of population size fluctuations.

This paper investigates the emergence and stability of 2-cycles for the Ricker model with the 2-year periodic Malthusian parameter. It is shown that the stability loss of the trivial solution occurs through the transcritical bifurcation resulting in a stable 2-cycle. The subsequent tangent bifurcation leads to the appearance of two new 2-cycles: stable and unstable ones. As a result, there is multistability. It is shown that the coexistence of two different stable 2-cycles is possible in a narrow area of the parameter space. Further stability loss of the 2-cycles occurs according to the Feigenbaum scenario.

This article researches model of two coupled an age structured populations. The model consists of two identical two-dimensional maps demonstrating the Neimark – Sacker and period-doubling bifurcations. The “bistability” of dynamic modes is found which is expressed in a co-existence the nontrivial fixed point and periodic points (stable 3-cycle). The mechanism of loss stability and formation of complex hierarchy for multistable states are investigated.