Relaxation oscillations in a kinetic model of catalytic hydrogen oxidation involving a chase on canards
Abstract A detailed study of two- and three-variable mathematical models of a heterogeneous catalytic system is presented with special attention to weakly stable dynamics, a type of complex irregular behavior frequently encountered in oscillating chemical reactions. One of the most important properties of the weakly stable dynamics is “a sensitive dependence on the initial conditions”. Our analysis of a global error in long-term numerical integration shows that a high sensitive dependence on the initial conditions appears in the three-variable system with fast, intermediate and slow variables due to existence of the canard cycles which occur close to Hopf bifurcation in the one-parameter family of two-variable subsystems.
With the FEM analysis soft ware NX Nastran,this paper achieves the buckling response analysis according to various structural dimension、work speed、disturbing force on the HSK tool system.The computing results and correlative conclusions can be regarded as the basis of structure stability and failure mechanism analysis,and provides the theoretical guidance HSK tool system's type selection and appropriately used in the high speed machining occasion.