Spatio†Temporal Spread Of Competitive Innovations: An Ecological Approach

This study proposes the continuous deterministic interaction model of the spread of a set of competitive innovations in space and time, and presents the Volterra†Lotka type vectorial differential equation of the diffusion process. Three major themes are considered: i) the competitive exclusion principle and the Markov chain's approximation of the diffusion process in the neighbourhood of equilibrium points, ii) the structure of competition based on the existence of explicit analytical formulas for the solution of the non†linear Volterra†Lotka type vectorial differential equation for the totally antagonistic approximation of the diffusion process within the vicinity of quasi equilibrium curves; and iii) the structure of the social and physical environment, the main extreme tendencies of behaviour of adoption units and places of the environmental niches, which are the focuses of resistance and support for different competing innovations.