  In this work, a class of continuous-time autonomous dynamical systems
describing many important phenomena and processes arising in real-world
applications is considered. We apply the nonstandard finite difference (NSFD)
methodology proposed by Mickens to design a generalized NSFD method for the
dynamical system models under consideration. This method is constructed based
on a novel non-local approximation for the right-side functions of the
dynamical systems. It is proved by rigorous mathematical analyses that the NSFD
method is dynamically consistent with respect to positivity, asymptotic
stability and three classes of conservation laws, including direct
conservation, generalized conservation and sub-conservation laws. Furthermore,
the NSFD method is easy to be implemented and can be applied to solve a broad
range of mathematical models arising in real-life. Finally, a set of numerical
experiments is performed to illustrate the theoretical findings and to show
advantages of the proposed NSFD method.
