Transition of neimark-sacker to flip bifurcation in a discrete prey-predator model with bazykin functional response and harvesting.

This paper discusses on the dynamics and bifurcations of a two-dimensional discrete prey-predator model with Bazykin functional response and linear harvesting in predator. Compared to Bazykin prey-predator model which focuses on competition for other resources, Bazykin functional response include predator competition for prey and predator saturation. Limited studies on Bazykin functional response especially in discrete model highlight the novelty of this research. A semi-discretisation method is applied to derive the model from continuous to discrete. The stability at each fixed point is summarised by applying related lemma and definition. The occurrences of Neimark-Sacker and flip bifurcations are established through the Centre Manifold Theorem and supported by numerical simulations. The coexistence fixed point first loses stability through Neimark-Sacker bifurcation before becoming stable over an intermediate parameter range. Then, the fixed point undergoes flip bifurcation giving rise to periodic and chaotic dynamics. Simulations by MATLAB and MATCONTM are included by providing the bifurcation, phase portrait and time series diagrams. The discrete model displays interesting dynamical behaviours such as transition of Neimark-Sacker to flip bifurcation, quasiperiodic oscillations, periodic solutions and chaos brought on by harvesting. This paper highlights that intensive harvesting leads to chaotic behaviour of prey population and subsequently lead to predator extinction. The results signifies that intensive harvesting combined with predator competition can drastically alter the system dynamics, offering crucial ecological insights into sustainable harvesting strategies.