Segura, JuanPerán Mazón, Juan Jacobo2025-06-252025-06-252020-02-01Daniel Franco, Juan Perán, Juan Segura. "Stability for one-dimensional discrete dynamical systems revisited. Discrete and Continuous Dynamical Systems - B, 2020, 25(2): 635-650". doi: 10.3934/dcdsb.20192581553-5231, ISSNe 1937-1179https://doi.org/10.3934/dcdsb.2019258https://hdl.handle.net/20.500.14468/26923This is an Accepted Manuscript of an article published by American Institute of Mathematical Sciences in "Discrete and Continuous Dynamical Systems - B (DCDS-B), 25(2). (2020)", available at: https://doi.org/10.3934/dcdsb.2019258We present a new method to study the stability of one-dimensional discrete-time models, which is based on studying the graph of a certain family of functions. The method is closely related to exponent analysis, which the authors introduced to study the global stability of certain intricate convex combinations of maps. We show that the new strategy presented here complements and extends some existing conditions for the global stability. In particular, we provide a global stability condition improving the condition of negative Schwarzian derivative. Besides, we study the relation between this new method and the enveloping technique.eninfo:eu-repo/semantics/openAccess12 Matemáticas33 Ciencias Tecnológicas53 Ciencias EconómicasartículoGlobal stabilitydiscrete dynamical systemenvelopingSchwarzian derivativepopulation model