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Multistability and multimodality in ricker’s model with genetically defined parameters

Keywords:

O.L. Zhdanova - Dr.Sc. (Phys.-Math.), Senior Research Scientist, Institute for Automation and Control Processes Far Eastern Branch of Russian Academy of Sciences. E-mail: axanka@iacp.dvo.ru E.Ya. Frisman – Corresponding Member of the Russian Academy of Sciences, Dr.Sc. (Biol.), Professor, Director, Complex Analysis of Regional Problems Institute Far Eastern Branch of Russian Academy of Sciences. E-mail: frisman@mail.ru


Mechanisms of stability loss and character of dynamics for uniform population have been investigated; at that the number of considered population is described by Ricker’s model with intrapopulation parameters defined on the genetic level under an influence of the natural selection. It has been shown that loss of stability by the nontrivial fixed points occurs only by the period-doubling bifurcation provided that the model parameters are inside the biological meaningful region. Effects of multistability and multimodality arise in some parametric regions. It has been shown, that along with a fixed point (dynamically stable or unstable) the circles of various length and chaotic attractors may exist in the model and it may be attractive for the system from some region of initial conditions. To measure the influence of initial conditions on the dynamics type and on the direction of the population evolution the basins of attraction for simultaneously existing asymptotic dynamic regimes has been constructed.
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