Emergence of diverse dynamical responses in a fractional-order slow-fast pest-predator model

To explore the impact of pest-control strategy on integrated pest management, a three-dimensional (3D) fractional- order slow-fast prey-predator model is introduced in this article. The prey community (assumed as pest) represents fast dynamics and two predators exhibit slow dynamical variables in the three-species interacting prey-predator model. In addition, common enemies of that pest are assumed as predators of two different species. Pest community causes serious damage to the economy. Fractional-order systems can better describe the real scenarios than classical-order dynamical systems, as they show previous history-dependent properties. We establish the ability of a fractional-order model with Caputo's fractional derivative to capture the dynamics of this prey-predator system and analyze its qualitative properties. To investigate the importance of fractional-order dynamics on the behavior of the pest, we perform the local stability analysis of possible equilibrium points, using certain assumptions for different sets of parameters and reveal that the fractional-order exponent has an impact on the stability and the existence of Hopf bifurcations in the prey-predator model. Next, we discuss the existence, uniqueness and boundedness of the fractional-order system. We also observe diverse oscillatory behavior of different amplitude modulations including mixed mode oscillations (MMOs) for the fractional-order prey-predator model. Higher amplitude pest periods are interspersed with the outbreaks of small pest concentration. With the decrease of fractional-order exponent, small pest concentration increases with decaying long pest periods. We further notice that the reduced-order model is biologically significant and sensitive to the fractional-order exponent. Additionally, the dynamics captures adaptation that occurs over multiple timescales and we find consistent differences in the characteristics of the model for various fractional exponents.