The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: 4n−2Cn/2−1rf ∑n j 1 xj/r n ∑ ik∈{0,1}, ∑n k 1 ik n/2 r2f ∑n i 1 −1 ik xi/r 4n·n−2Cn/2−1 ∑n i 1 f xi , where n ≥ 2, r ∈ R r2 / n and f is a mapping. And we prove that the e...

In this brief note, it is shown that the random hyperbolicity of a random linear cocycle is equivalent to having the Lipschitz shadowing property.

In this brief note, it is shown that the random hyperbolicity of a random linear cocycle is equivalent to having the Lipschitz shadowing property.

Infinite population models of co-evolutionary dynamics are useful mathematical constructs hinting at the possibility of a wide variety of possible dynamical regimes from simple attractive fixed point behavior, periodic orbits to complex chaotic dynamics. We propose to use the framework of shadowing lemma to link such mathematical constructs to large finite population computer simulations. We al...