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In this work, we deal with general reactive systems involving N species and M elementary reactions\udunder applicability of the mass-action law. Starting from the dynamic variables introduced in two\udprevious works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138(23), 234101 (2013); 138(23),\ud234102 (2013)], we turn to a new representation in which the system state is specified in a (N x M)^2-\uddimensional space by a point whose coordinates have physical dimension of inverse-of-time. By\udadopting hyper-spherical coordinates (a set of dimensionless “angular” variables and a single “radial”\udone with physical dimension of inverse-of-time) and by examining the properties of their evolution\udlaw both formally and numerically on model kinetic schemes, we show that the system evolves\udtowards the equilibrium as being attracted by a sequence of fixed subspaces (one at a time) each\udassociated with a compact domain of the concentration space. Thus, we point out that also for general\udnon-linear kinetics there exist fixed “objects” on the global scale, although they are conceived in such\udan abstract and extended space. Moreover, we propose a link between the persistence of the belonging\udof a trajectory to such subspaces and the closeness to the slow manifold which would be perceived\udby looking at the bundling of the trajectories in the concentration space

Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system