A chaotic study of love dynamics with competition using fractal-fractional operator

Abstract

Purpose

The objective of this work is to analyze the necessary conditions for chaotic behavior with fractional order and fractal dimension values of the fractal-fractional operator.

Design/methodology/approach

The numerical technique based on the fractal-fractional derivative is implemented over the fractional model and analyzes the condition at the distinct values of fractional order and fractal dimension.

Findings

The obtained numerical solution from the numerical technique is analyzed at distinct fractional order and fractal dimension values, and it has been figured out that the behavior of the solution either chaotic or non-chaotic agrees with the condition.

Originality/value

The necessary condition is associated with the fractional order only. So, our work not only studies the condition with fractional order but also examines the model by simultaneously adjusting fractal dimension values. It is found that the model still has chaotic or non-chaotic behavior at certain fractal dimension values and fractional order values corresponding to the condition.

Citation

Kumar, A., Shaw, P.K. and Kumar, S. (2024), "A chaotic study of love dynamics with competition using fractal-fractional operator", Engineering Computations, Vol. 41 No. 7, pp. 1884-1907. https://doi.org/10.1108/EC-02-2024-0151