This paper considers numerical methods for stability analyses of periodic solutions of ordinary differential equations. Stability of a periodic solution can be determined by the corresponding monodromy matrix and its eigenvalues. Some commonly used numerical methods can produce inaccurate results of them in some cases, for example, near bifurcation points or when one of the eigenvalues is very ...

In this paper, we will derive some twist criteria for the periodic solution of a periodic scalar Newtonian equation using the third order approximation. As an application to the forced pendulum ẍ + ω2 sinx = p(t), we will find an explicit bound P (ω) for the L1 norm, ‖p‖1, of the periodic forcing p(t) using the frequency ω as a parameter such that the least amplitude periodic solution of the fo...

This paper is concerned with an almost periodic Volterra integro dynamic equation on time scales. Based on the theory of calculus on time scales, by using differential inequality theory and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the global attractivity of the system are obtained. Then, by using the properties of almost periodic func...