arXiv subjects

Rajesh Ranjan Patra

Publications and source records attributed to Rajesh Ranjan Patra.

3 recordsLinked to original sources

arXiv2024

Double Allee effect induced extinction and bifurcation in a discrete predator-prey model

The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a discrete predator-prey model where the prey population is associated with two component Allee effects. We derive sufficient conditions for the existence and local stability nature of the fixed points of the system. The occurrence of Neimark-Sacker bifurcation is established, and sufficient conditions are obtained along with the normal form. Numerically, we demonstrate that the system exhibits Neimark-Sacker bifurcation for various system parameters. Additionally, the numerical simulations indicate that certain system parameters have threshold values, above or below which the populations are driven to extinction due to the effect of the double Allee effect.

math.DS↗

arXiv2024

Discontinuous harvesting policy in a Filippov system involving prey refuge

In this article, a non-smooth predator-prey dynamical system is considered. Here, we discuss about sustainable harvesting in a Filippov predator-prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local sliding bifurcations are also observed for the system. Numerical simulations are presented to illustrate the dynamical behaviour of the system.

math.DS↗

arXiv2022

Effect of delay and control on a predator-prey ecosystem with generalist predator and group defence in the prey species

Generalist predators consist an important component of an ecosystem which may act as a biocontrol agent and influence the dynamics significantly. In this paper, we have studied the effect of delayed logistic growth of the prey species with group defence behaviour. The Lyapunov stability criteria for the interior equilibrium point is derived. Also, the condition of Hopf-bifurcation and the point of bifurcation are obtained. The length of the delay is also estimated for the system to preserve stability. Numerical simulations are performed and illustrated to support the obtained analytical results. Using a feedback control mechanism, the stability of the unstable equilibrium point is restored. Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis, which is an efficient tool often employed in uncertainty analysis, is used to explore the entire parameter space of a model.

math.DS↗