In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in . 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.

In this article, the effect of the magnetic field, initial stress, rotation, and nonhomogeneity on the radial displacement and the corresponding stresses in orthotropic material is investigated. The analytical solution for the elastodynamic equation is solved in terms of displacements. The variation of stresses, displacement, and perturbation magnetic field have been shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, the rotation, and nonhomogeneity.

Our aim in this paper is to obtain formulas for solutions of rational difference equations such as $x_{n+1}=1\pm \left(x_{n-1}{y}_n\right)/\left(1-y_n\right),$$y_{n+1}=1\pm \left(y_{n-1}{x}_n\right)/\left(1-x_n\right),$ and $x_{n+1}=1\pm \left(x_{n-1}{y}_{n-2}\right)/\left(1-y_n\right),$$y_{n+1}=1\pm \left(y_{n-1}{x}_{n-2}\right)/\left(1-x_n\right),$ where the initial conditions $x_{-2}$, $x_{-1}$, $x_0$, $y_{-2}$, $y_{-1}$, $y_0$ are non-zero real numbers. In addition, we show that the some of these systems are periodic with different periods. We also verify our theoretical outcomes at the end with some numerical applications and draw it by using some mathematical programs to illustrate the results.

The present paper deals with the study of the wave propagation in a homogeneous transversely isotropic magneto-thermo-piezoelectric cylindrical material, under the influence of rotation, in the context of the linear theory of thermoelasticity. The displacement, electric potential, magnetic potential, electrostatic displacement, and magnetic induction functions are introduced to uncouple the equations of motion, with boundary conditions. After deriving secular equations in closed form and isolated mathematical conditions, the effect of rotation, phase velocity, attenuation coefficient profiles and relative frequency shift on dispersion curves is studied. The study is very helpful in the development of rotation sensors and other piezoelectric devices. The numerical results of the physical quantities have been illustrated graphically.

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.