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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 تیر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93606.1650

نویسندگان

Aida Bellout Bellout¹؛ Rabah Bououden^{1، 2}؛ Seyf El Islam Bouzeraa²؛ Messaoud Berkal^{* 3}

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

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

³Department of Applied Mathematics, Abdelhafid Boussouf University Center, Mila ,R.P 26, Mila, 43000, Algeria.

چکیده

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 version, 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 exhibits 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 fractional maps offer a practical alternative for simulating chaotic systems in real-time applications.

کلیدواژه‌ها

Fractional difference equations؛ Gauss map؛ Fixed memory length؛ Bifurcation and chaos؛ Lyapunov exponent