A.U. Perevarukha

Article considers different chaotic modes of mathematical biology models. Particular qualities of routs to chaos for two previously proposed stock-recruitment models are studied. It is proved, that explored Ricker and Shepard model inconsistent from the point of view of their biological interpretation, and mutually exclude correctness of each other. The further studies of the nonlinear phenomena in those models were closely related with appearance of periodic windows. It is shown, why in models appear tangent bifurcations and the following subduction of strange attractor on example of window with cycle of period 3. Presence of the cycle of period 3 the important features for discrete dynamic system. From conclusion of the proved Sharkovskii theorem succeed that period 3 imply chaos. The region of chaotic motion, witch appeared after period-doubling bifurcations of period 3 cycle presents itself three disjoint bands in the phase space. Chaotic attractor would be restored after interior crisis, when size of attractor suddenly widened. In the dynamics of functional iterations which often used for simulation can exist complexly nonlinear phenomena, not taken into account in step of buildings of the single population models or community of the several different fish spices. Those nonlinear phenomena, such as crisis and subduction of attractors, chaotic transient and intermittency has undoubtedly influence on the biological interpretation of the result of computer simulation. More perfect and explicated type of the hybrid stock-recruitment mathematical model elaborated based on of influence of step-wise changes in early ontogenesis of anadromous fish species according to positions of the theory of development of organisms. Model is implemented in form of hybrid automaton. Model has allowed to describe the wave-like stock-recruitment dependency. New model required for study Caspian See population of sturgeon. In new model exist regular attractors, but the boundaries of basins of attraction become fractal-like. Thereby exists notattracting chaotic set and model is characterized by final state sensitivity. We shall not be able to predict stable condition of the population after abandonment of chaotic repeller.