Asymptotic behavior of a planar dynamic system

Asymptotic Behavior of a Planar Dynamic System

We investigate the asymptotic solutions of the planar dynamic systems and the second order equations on a time scale by using a new version of Levinson’s asymptotic theorem. In this version the error estimate is given in terms of the characteristic (Riccati) functions which are constructed from the phase functions of an asymptotic solution. It means that the improvement of the approximation dep...

Dynamic Behavior Analysis of a Planar Four-bar Linkage with Multiple Clearances Joint

 In practice, clearances in the joints are inevitable due to tolerances, and defects arising from design and manufacturing. In the presence of clearance at a joint, a mechanism gains some additional, uncontrollable degrees of freedom which are the source of error. Moreover, joints undergo wear and backlashes and so cannot be used in precision mechanisms. In this study, the dynamic behaviour of ...

Asymptotic behavior of a system of two difference equations of exponential form

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

Asymptotic Behavior of a Periodic Diffusion System

Asymptotic behavior of second-order dynamic equations

We prove several growth theorems for second-order dynamic equations on time scales. These theorems contain as special cases results for second-order differential equations, difference equations, and q-difference equations. 2006 Elsevier Inc. All rights reserved.