In this paper, we are going to approximate the Dynamical system of the SIR mathematical model, numerically. The expression for basic reproduction number R0 is obtained which plays main role in the local and global stability. On the other hand, if R0 > 1 then the equilibrium point is unstable. Our numerical simulations show that our proposed NSFD method provides reliable and consistent, positive and converging results at all step sizes as compared to the traditional RK-4 method and Euler method which diverge at large step sizes and produce negative and unstable results with large oscillations. The local stability of the equilibrium point is proved by Jacobean method,however, Schur-Cohn conditions are used to discuss the local stability for the discrete NSFD scheme. To prove the global stability of equilibria, the Enatsu criterion and Lyapunov function are used. This paper presents theoretical findings and numerical simulations that can be used as a powerful instrument for forecasting the spread of added infectious illnesses.

A method for asymptotic stability of adaptive controllable Dynamical systems, including the necessary and sufficient conditions for this method, is discussed. The method is applied to the predator- prey map to illustrate the theoretical result.

In this paper, Front Engine Accessory Drive (FEAD) system of automotive engine is modeled with ADAMS software. The model is validated using engine test data. It is then used to investigate the effect of design parameters on the system performance such as belt vibration and loads on the idlers. Three alternative layouts were developed in order to improve the performance of original EEAD system. The validated model was used to study the effect of changes made to the layouts on the reduction of vibration and loads. Several system outputs indicated that for the modified layouts, large reductions in vibration and loads were achieved. It was concluded that one of proposed layouts was more appropriate and could be a useful substitution to the original layout. The developed model also proved useful for the design of engine FEAD systems and could be used for further developments.

We present a numerical study of a one-dimensional version of the Burridge- Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making only small time-dependent perturbations. If part of the system (i.e., both ends) is wiggled by imposing the periodic force, then it is possible to approach the nearly stable solution even in a system which would otherwise be chaotic. The solutions are periodic in both time and space and display effects that are strikingly similar to those seen experimentally and numerically by Starrett and Tagg [6], Johnson et al. [7] and others. This case is very important in controlling chaos, reducing the noise in a noisy system and Dynamical lubrication. We observe that for an arbitrary disordered set of initial conditions, the system can spontaneously organize itself so that the stable nearly periodic solutions emerge in a proper time. The average of power input is reduced in a sensitive way and a regular, stable, noise-free behaviour appears. The nature of the boundary conditions on the ends of the chain has a strong effect on the nature of the solutions and requires the parameters to be tuned in a proper way. We also study the possibility of taming spatiotemporal chaos with disorder and investigate the effect of broken symmetry in the system.