A study on efficient chaotic modeling via fixed-memory length fractional Gauss maps

Document Type : Research Article

Authors

• A. Bellout ¹
• R. Bououden ^{1, 2}
• S.E.I. Bouzeraa ²
• M. Berkal ²

¹ Laboratory of Mathematics and their Interactions, Department of Mathematics, Abdelhafid Boussouf University Center, Algeria.

² Department of Applied Mathematics, Abdelhafid Boussouf University Center, Mila ,R.P 26, Mila, 43000, Algeria.

10.22067/ijnao.2025.93606.1650

Abstract

This paper investigates the dynamic behavior of the fractional Gauss map with fixed memory length, highlighting its potential for efficient chaotic modeling. Unlike classical fractional systems that require the full history of states, the proposed approach introduces a memory-limited ver-sion, significantly reducing computational cost while preserving complex dynamical features. Through bifurcation analysis, Lyapunov exponents, and the $0 − 1$ test for chaos, the study demonstrates that the system ex-hibits a rich variety of behaviors, including periodic, quasi-periodic, and chaotic regimes, depending on the fractional order and memory size. A comparative evaluation with the classical Gauss map reveals that the fixed-memory model retains similar chaotic characteristics, but with improved computational efficiency. These findings suggest that fixed-memory frac-tional maps offer a practical alternative for simulating chaotic systems in
real-time applications. 

Keywords

• Chaos
• Fractional difference equations
• Gauss map
• Fixed memory length
• Bifurcation
• Lyapunov exponent

Main Subjects

• Computational Mathematics

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