A Chaotic Study of Fractional Order Host-Parasitoid Competition Model of Ecology

In this paper, we have extended a classical mathematical model of contact spread infection based on the one-host two parasitoid competition model with fractional order values to account for the spread of infection. We have investigated contact spread infection of pathogen transmission on the host-parasitoid competition model using Caputo and fractal–fractional C–F fractional derivatives. Fractal–fractional operators improve the predictive capacity of infection by utilizing the memory effect. We have calculated the existence and uniqueness of the proposed fractional competition model. Moreover, this study exhibits the chaotic behavior under different values of fractional order and parameters based on the possibility of obtaining new chaotic behaviors. We have illustrated some maximal bifurcation diagrams of the fractional competition model with different parameter values. Numerical outcomes are carried out by two numerical schemes: Adams-Bashforth and Newton polynomial based technique, with Caputo and Caputo–Fabrizio (C–F) fractional operators. We have gained some useful insights about the fractional host-parasitoid competition model at various parameters and fractional orders based on the graphical results. In contact spread infections, transient and long-term dynamics are highly complex, as shown by computational simulations and steady-state analyses. Using this model for integer and non-integer orders, we can gain a better understanding of the complexity of the host-parasitoid competition model.