One-Dimensional Dynamics

Abstract

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Generalized Models from Beta(p, 2) Densities with Strong Allee Effect: Dynamical Approach

“…For the parameter values, such that these conditions hold, the associated dynamic behaviour is characterized by bifurcations (period doubling) and chaos, verifying Sharkovsky's Theorem, a non-decreasing function in order to the parameter r i , [1], [4] and [5]. In turn, the chaotic region ends at the designated "fullshift", whose symbolic sequence is CRL ∞ .…”

“…The topological complexity of a dynamical system is usually measured by its topological entropy, see [3], [4], [5] and references therein.…”

“…For a more detailed approach about subshifts of finite type and the Perron-Frobenius Theorem for Markov transition matrix, see [3], [4] and references therein.…”

“…• Monotonicity of the topological entropy: if the intrinsic growth rate r i increases, then the topological entropy is a non-decreasing function in order to r i , (consequence of the negative Schwartzian derivative), [4] and [5].…”

Number of Equilibrium States of Piecewise Monotonic Maps of the Interval

“…We recall that continuity is not sufficient for uniqueness even for a subshift of finite type (see [10,Chapter 2] We outline the (easy) proof: (**) implies that each irreducible part of f is finite so that each TTS is bounded away from the critical points; / C2 implies that the diameters of P" restricted to a TTS decrease exponentially with « by [7 Set Fn -i(E"). Fn is («, ¿)-separated but may be non-maximal.…”