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<p>This article investigates generalized synchronization among chaotic systems of varying dimensions. The analysis begins with integer-order chaotic systems, progresses to fractional-order systems, and subsequently addresses time-delayed chaotic systems. For each case, sufficient conditions for achieving generalized synchronization are derived. Control analysis is conducted using feedback control methods and finite-time controllers to enable a comprehensive comparison of results. The discussion also extends to generalized synchronization in discrete chaotic maps, with several related theorems presented. Fractional calculus, widely adopted in mathematics and physics, extends differentiation and integration concepts to non-integer orders. Fractional-order chaotic systems are characterized by a memory effect, a property absent in integer-order systems. Numerical simulations confirm the theoretical results across the scenarios examined in this study.</p>

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Generalized synchronization between coupled integer, fractional and delay chaotic systems

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Vijay K. Shukla,
  • Mahesh C. Joshi,
  • Prashant K. Mishra,
  • Changjin Xu

摘要

This article investigates generalized synchronization among chaotic systems of varying dimensions. The analysis begins with integer-order chaotic systems, progresses to fractional-order systems, and subsequently addresses time-delayed chaotic systems. For each case, sufficient conditions for achieving generalized synchronization are derived. Control analysis is conducted using feedback control methods and finite-time controllers to enable a comprehensive comparison of results. The discussion also extends to generalized synchronization in discrete chaotic maps, with several related theorems presented. Fractional calculus, widely adopted in mathematics and physics, extends differentiation and integration concepts to non-integer orders. Fractional-order chaotic systems are characterized by a memory effect, a property absent in integer-order systems. Numerical simulations confirm the theoretical results across the scenarios examined in this study.