Discrete-Time Predator-Prey Model with Bifurcations and Chaos

In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in ℝ+2. It is proved that the model has a trivial fixed point for all parametric values and the unique positive fixed point under definite parametric conditions. By the existing linear stability theory, we studied the topological classifications at fixed points. It is explored that at trivial fixed point model does not undergo the flip bifurcation, but flip bifurcation occurs at the unique positive fixed point, and no other bifurcations occur at this point. Numerical simulations are performed not only to demonstrate obtained theoretical results but also to tell the complex behaviors in orbits of period-4, period-6, period-8, period-12, period-17, and period-18. We have computed the Maximum Lyapunov exponents as well as fractal dimension numerically to demonstrate the appearance of chaotic behaviors in the considered model. Further feedback control method is employed to stabilize chaos existing in the model. Finally, existence of periodic points at fixed points for the model is also explored

On Free Vibrations of Elastodynamic Problem in Rotating Non-Homogeneous Orthotropic Hollow Sphere

The effect of non-homogenity and rotation on the free vibrations for elastodynamic problem of orthotropic hollow sphere is discussed. The free vibrations are studied on the basis of the linear elasticity. The determination is concerned with the eigenvalues of the natural frequency for mixed boundary conditions. The numerical results of the frequency equations are discussed in the presence and absence of non-homogenity and rotation. The computer simulated results indicate that the influence of non-homogenity and rotation in orthotropic material is pronounced