K. Sathiyanathan

In this article, we propose the Holling type‐II predator‐prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed model. Next, we also establish the local stability and Hopf bifurcation analysis for the corresponding delayed model. Finally, we discuss how cannibalism and delay play an important role in stabilizing and destabilizing the proposed system both theoretically and numerically.

The discrete‐time system has more complex and chaotic dynamical behaviors as compared to the continuous‐time system. This paper extends a discrete Leslie–Gower predator‐prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.

This paper is concerned with the controllability of higher order fractional damped delay dynamical systems with time varying multiple delays in control, which involved Caputo derivatives of any different orders. A necessary and sufficient condition for the controllability of linear fractional damped delay dynamical system is obtained by using the Grammian matrix. Sufficient conditions for controllability of the corresponding nonlinear damped delay dynamical system has established by the successive approximation technique. Examples have provided to verify the results.