Comments on 'Analysis and application of a novel three-dimensional energy-saving and emission-reduction dynamic evolution system' [Energy 40 (2012) 291-299]

摘要

In the commented paper the authors propose a novel three-dimensional energy-saving and emission-reduction system. They claim to prove the existence of Silnikov homodinic orbits by using the undetermined coefficient method and, consequently, the Silnikov theorem guarantees that the system has Smale horseshoes and the horseshoe chaos. Unfortunately, their demonstration is invalid because the form of the function they assume in the series expansion for the homodinic orbits is incorrect. Namely, they compose the homodinic orbit of the same manifold, which is stable in forward time and unstable in reverse time.