Abstract:
Author discusses modelling of transition from stable equilibrium to a transitive chaotic mode in nonlinear dynamic system for a case when there is no occurrence of the cascade of topological nonequivalent phase portraits if parameter is varied continuously. New dynamic system defined as $\mathrm{R}_n+1=\psi(\mathrm{R}_n)$ with existents of $4$ nontrivial stationary points is suggested. Elaborated hybrid stock-recruitment mathematical model 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 shows chaotic dynamics owing to occurrence of complex basin boundaries of two attractors, not being smooth manifolds.
Keywords:nonattracting chaotic sets, modelling of population dynamics, hybrid representation of time.
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