STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL

作     者：Rakesh KUMAR Anuj Kumar SHARMA Kulbhushan A GNIHOTRI 

作者机构：Department of Applied Sciences S.B.S. State Technical Campus Ferozepur Punjab 152004 India Research Scholar with I.K.G. Punjab Technical University Kapurthala Punjab 144603 India Department of Mathematics L.R.D.A. V. College Jagraon Ludhiana Punjab 142026 India 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2018年第38卷第2期

页      面：709-732页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：the Support Provided by the I.K.G. Punjab Technical University Kapurthala Punjab India where one of us(RK) is a Research Scholar 

主　　题：Innovation diffusion model stability analysis Hopf-bifurcation normal form theory center manifold theorem 

摘      要：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, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.