Basin Structure and Unpredictability in a Two-Dimensional Memristor-Based Cubic Map

Abstract

This study investigates the dynamics of a two-dimensional memristor-based cubic map, with emphasis on the structure of its basins of attraction and the unpredictability of its long-term behavior. A recurrence-based automated method is employed to identify attractors without prior knowledge of their locations, which enables a comprehensive analysis of multistability. The resulting basin structures exhibit fractal boundaries and regions of divergence, reflecting a high sensitivity to initial conditions. To quantify the complexity of the attractor basins, basin entropy values are evaluated across various parameter sets as a measure of the system’s unpredictability. The results show regions of high basin entropy, which highlight the emergence of intricate fractal-like basin boundaries and robust chaotic behavior. These findings suggest that memristive elements can enhance complexity and unpredictability in discrete dynamical systems, with potential applications in the design of secure and resilient digital systems that exploit chaotic dynamics.

Keywords

• Basins of attraction
• Memristive systems
• Multistability
• Uncertainty exponent

İki Boyutlu Memristör Tabanlı Kübik Haritada Havza Yapısının ve Öngörülemezliğin Analizi

Abstract

Bu çalışma, iki boyutlu memristör tabanlı bir kübik haritanın dinamiklerini, özellikle çekici havzalarının yapısı ve uzun vadeli davranışının öngörülemezliği üzerinde durarak incelemektedir. Sistem parametreleri değiştirildikçe, periyodik, kaotik ve hiperkaotik rejimler arasındaki geçişler çatallanma diyagramları, Lyapunov üssü hesaplamaları ve sayısal benzetimler kullanılarak analiz edilmiştir. Çekicilerin konumlarına dair ön bilgi gerektirmeyen rekürans tabanlı otomatik bir yöntem kullanılarak çekiciler tanımlanmıştır. Bu yaklaşım, çoklu kararlılık durumlarının ayrıntılı olarak incelenmesini mümkün kılmıştır. Elde edilen havza yapıları, fraktal sınırlar ve sapma bölgeleri sergileyerek başlangıç koşullarına karşı yüksek hassasiyet göstermektedir. Elde edilen bulgular, memristif elemanların ayrık dinamik sistemlerdeki karmaşıklığı ve öngörülemezliği artırabileceğini ortaya koymaktadır. Bu sonuçlar, kaotik davranışları temel alan güvenli ve dayanıklı sayısal sistemlerin geliştirilmesine yönelik çalışmalara katkı sunabilir.

Keywords

• Çekici havzaları
• Memristif sistemler
• Çoklu kararlılık
• Belirsizlik üssü

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