A fractional-order love dynamical model with a time delay for a non-synergic couple: stability analysis and Hopf bifurcation

Abstract

In this manuscript, we have investigated the fractional-order love dynamic model with a time delay for non-synergic couples. The asymptotic stability of the model's equilibrium points has been studied during the quantitative analysis of the model and Hopf bifurcation analysis has been done for the model by using Laplace transformation technique. Stability analysis is an established tool for the analysis of complex mathematical models. Numerous studies have examined the model for integer order, but none have examined the fractional-order model under the impact of time delay and done stability and Hopf bifurcation analysis for the aforesaid model. This motivates us to study the fractional-order delay love dynamical model for non-synergic couple. Here, we have considered the fractional- order time delay to represent the long-term behaviour of the model. Finally, the numerical simulations have been carried out using MATLAB to illustrate our derived results.