Experimenting with Discrete Dynamical Systems

2023/06/20 by George Spahn, Doron Zeilberger, Spahn, George +1
Computer Science · Mathematics · Medicine · #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Numerical methods for differential equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2306.11929

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate the power of Experimental Mathematics and Symbolic Computation to study intriguing problems on rational difference equations, studied extensively by Difference Equations giants, Saber Elaydi and Gerry Ladas (and their students and collaborators). In particular we rigorously prove some fascinating conjectures made by Amal Amleh and Gerry Ladas back in 2000. For other conjectures we are content with semi-rigorous proofs. We also extend the work of Emilie Purvine (formerly Hogan) and Doron Zeilberger for rigorously and semi-rigorously proving global asymptotic stability of arbitrary rational difference equations (with positive coefficients), and more generally rational transformations of the positive orthant of R^k into itself

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