Tricriticality and chaos in a generalized Allee-logistic map

2026/06/03 by Marcelo A. Pires, José S. Andrade, Hans J. Herrmann · 1 voice
Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #nlin.CD #physics.comp-ph #physics.soc-ph #q-bio.PE

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Abstract

We present a novel nonlinear dynamical model, the generalized Allee-logistic (GAL) map given by x_t+1 = r x_t (1 - x_t) G(x_t) where G(x_t) = m (x_t - h) + 1 - m incorporates the Allee effect with magnitude m and threshold h. The case m = 0 yields the logistic map with a continuous transition to extinction. Conversely, m = 1 recovers a previously studied model that undergoes only a discontinuous extinction-to-active transition. Between these extremes, the GAL map exhibits nontrivial phenomena, including tricriticality with a closed-form expression for the tricritical point and a universal crossover function. Under a small external input, we verify Widom-like relations. We also note that the Allee effect disfavors the onset of chaos. Our work establishes additional bridges between analytically tractable chaotic maps, nonequilibrium tricriticality, and Allee effects.

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Discussions

• Marcelo A. Pires, Jos\'e S. Andrade Jr., Hans J. Herrmann: Tricriticality and chaos in a generalized Allee-logistic map https://arxiv.org/abs/2606.05351 https://arxiv.org/pdf/2606.05351 https://arxiv. [bsky, 0 points, 0 comments]

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