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Chaotic behavior in a class of one-dimensional maps. (English) Zbl 0827.58038

Summary: In this work, mechanisms of transition into chaotic behavior in a slightly generalized form of the Verhulst map, \(x_{n + 1} = \lambda x^\alpha_n (1 - x_n)^\beta\), \(0 \leq x_n \leq 1\), \(\alpha > 0\), \(\beta > 0\), \(\lambda > 0\) are numerically studied. Transition to chaos via both the period doubling and intermittency routes are observed. The invariant distribution is studied, the nature of an observed attractor is clarified.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37E99 Low-dimensional dynamical systems
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