Dynamical analysis of an innovation diffusion model with evaluation period

Abstract

A nonlinear form of innovation diffusion model consisting of two driving equations governed by two variables namely adopter and non-adopter population density is proposed to lay stress on the evaluation period. The model is analyzed qualitatively with stability theory, Hopf-bifurcation analysis by taking evaluation period as a control parameter to see the role of evaluation period in shaping the dynamics of adopter and non-adopters. The threshold value of evaluation period is determined beyond which small amplitude oscillations of adopter and non-adopter population occur and goes on decreasing with the increase in carrying capacity of non-adopter class. The sensitivity analysis of the state variables w.r.t. the model parameters is performed at a non-zero equilibrium point. The effect of external influences to achieve maturity stage is also discussed. The analytical results so obtained are verified through numerical simulations by using the Matlab software.