Dissipative maps at the chaos threshold: numerical results for the single-site map

2001/09/17 by Uǧur Tırnaklı, Ugur Tirnakli · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #CHAOS (operating system) #Chaos control and synchronization #Chaotic #Computer science #Control theory (sociology) #Coupled map lattice #Dissipative system #Edge of chaos #Mathematics #Physics #Quantum chaos and dynamical systems #Standard map #Statistical Mechanics and Entropy #Statistical physics #Synchronization of chaos #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1016/s0378-4371(01)00649-5

8 pages with 4 figures, submitted to Physica A

arxiv created 2001/09/17 · openalex publication_date 2002/03/01 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We numerically study, at the edge of chaos, the behaviour of the sibgle-site map x_t+1=x_t-x_t/(x_t²+γ²), where γ is the map parameter.

Citations

• Circular-like maps: sensitivity to the initial conditions, multifractality and nonextensivity
• Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
• Asymmetric unimodal maps: Some results fromq-generalized bit cumulants

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• Histoire et civilisation au Château Ramezay
• Asymmetric unimodal maps at the edge of chaos