Stability and Hopf Bifurcation Analysis of a Delayed Innovation Diffusion Model with Intra-Specific Competition

Abstract

This article is concerned with the diffusion of a sport in a region, and the innovation diffusion model comprising of population classes, viz. nonadopters class, information class and adopters class. A qualitative analysis is carried out to assess the global asymptotic stability of the interior equilibrium for null delay. It has also been proved that the parameter [Formula: see text] (age gaps among sportspersons) in the intra-specific competition between the new players and the senior players can even destabilize the otherwise globally stable interior equilibrium state and the coexistence of all the populations is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and center manifold arguments, the stability of bifurcating periodic orbits is determined. Numerical simulations have been executed in support of the analytical findings.

Multiple dynamics in a delayed predator‐prey model with asymmetric functional and numerical responses

“…The case of bistability also exists in predator‐prey model when time delay is incorporated in the fear effect of prey due to predator 22 . Kumar and Sharma 23 have considered a population model of senior players and new players in any sports. They proved that time delay due to age gap of the players in the intra‐specific competition among the players can destabilize even a globally stable interior equilibrium.…”