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<p>This paper introduces the competition component to Sprott's nonlinear love triangle model and observes that the new system likewise exhibits chaotic behaviour. In order to make the model more realistic, we have modified the existing fractional-order system using exponential decay memory. The occurrence of fractional systems proves the validity of this generalization with memory, since memory impacts romantic relationships over time. The considered model is assessed by using Caputo-Fabrizio fractional derivatives, and the fractional Adams-Bashforth numerical approach is used to solve the system based on Lagrange polynomial interpolation. Existence, uniqueness, and Ulam–Hyers stability are established through fixed-point theory and nonlinear analysis. Further, the error analysis of the current method has also been incorporated. Finally, numerical simulations are used to demonstrate the behaviour of the solution using graphical representations.</p>

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Fractional Order Love Triangle System: An Analysis with Exponential Decay Memory

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Rajarama Mohan Jena,
  • Snehashish Chakraverty

摘要

This paper introduces the competition component to Sprott's nonlinear love triangle model and observes that the new system likewise exhibits chaotic behaviour. In order to make the model more realistic, we have modified the existing fractional-order system using exponential decay memory. The occurrence of fractional systems proves the validity of this generalization with memory, since memory impacts romantic relationships over time. The considered model is assessed by using Caputo-Fabrizio fractional derivatives, and the fractional Adams-Bashforth numerical approach is used to solve the system based on Lagrange polynomial interpolation. Existence, uniqueness, and Ulam–Hyers stability are established through fixed-point theory and nonlinear analysis. Further, the error analysis of the current method has also been incorporated. Finally, numerical simulations are used to demonstrate the behaviour of the solution using graphical representations.