Stability and bifurcation analysis of a delayed innovation diffusion model |
| |
Authors: | Rakesh KUMAR Anuj Kumar SHARMA Kulbhushan AGNIHOTRI |
| |
Affiliation: | 1. Department of Applied Sciences, S.B.S. State Technical Campus, Ferozepur, Punjab 152004, India;2. Research Scholar with I.K.G. Punjab Technical University, Kapurthala, Punjab 144603, India |
| |
Abstract: | In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage (time delay) is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period (time delay, τ) passes through a critical value. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included. |
| |
Keywords: | Innovation diffusion model stability analysis Hopf-bifurcation normal form theory center manifold theorem 34C23 34D20 37L10 |
本文献已被 CNKI ScienceDirect 等数据库收录! |
|