A study on qualitative analysis of a discrete fractional order prey-predator model with intraspecific competition

Abstract

The interaction of predators and prey is seen as a natural occurrence in biological systems. This paper investigates a predator-prey model with fractional derivatives. A term that models intraspecific competition within the predator population is also included in our proposed model with relation to the fractional derivative of Caputo. For large predator-to-prey density ratios, this extra term restricts the growth of the predator population. The topological structure of the fixed points is studied in this paper. Mathematically we prove that the considered model experiences both a Neimark-Sacker (NS) and a Period-doubling (PD) bifurcation under specific parametric conditions. We investigate the presence of a period-doubling bifurcation and a Neimark-Sacker bifurcation using the bifurcation theory. The dynamic behavior of this model is examined based on changes made to the control parameters and influenced by the initial conditions. The main features of numerical simulations, such as phase portraits, maximal Lyapunov exponents, and bifurcation diagrams, are shown to demonstrate the richer and more complicated dynamics, complex dynamical behaviors, and the accuracy of theoretical analysis. Furthermore, two methods of chaos management are applied in order to reduce the chaos that the system inherently contains.