On the Dynamics of Particular Discrete Quadratic Systems with Potential Absence of Equilibria: Standard Euler versus Nonstandard Mickens Discretizations
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6506Keywords:
Nonstandard difference scheme, Dynamical system, Two-parameter bifurcation diagramAbstract
This study examined the dynamics of a three-dimensional discrete-time quadratic system that may lack equilibrium points, depending on the parameter values. Two discretization methods were considered: the standard forward Euler method and a nonstandard finite-difference scheme following Mickens’ approach. We investigated how the control parameter and step size af-
fect stability and transition to chaos. Analytical derivations, together with numerical experiments including phase portraits, bifurcation diagrams, and Lyapunov exponent calculations, reveal diverse dynamic behaviors. Both discretizations capture chaotic motion, but the nonstandard finite-difference scheme preserves structural stability more effectively across parameter ranges. These results enrich the study of discrete chaotic systems and highlight the advantages of nonstandard discretization.
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Copyright (c) 2025 Moch. Fandi Ansori, Hafidh Khoerul Fata, Nurcahya Yulian Ashar, Ratna Herdiana, Khairul Saleh
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