TY - JOUR
T1 - Delay Induced Hopf Bifurcation in a Nonlinear Innovation Diffusion Model: External Influences Effect
AU - Rakesh Kumar, Anuj K. Sharma & Kulbhushan Agnihotri
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 422
EP - 446
PY - 2018
DA - 2018/08
SN - 8
DO - http://doi.org/10.4208/eajam.010417.200118
UR - https://global-sci.org/intro/article_detail/eajam/12617.html
KW - Evaluation period, stability analysis, Hopf bifurcation, normal form theory, center manifold theorem.
AB - <p style="text-align: justify;">A nonlinear innovation diffusion model which incorporates the evaluation
stage (time delay) is proposed to describe the dynamics of three population classes for
non-adopter and adopter densities. The local stability of the various equilibrium points
is investigated. It is observed that the system is locally asymptotically stable for a delay
limit and produces periodic orbits via a Hopf bifurcation when evaluation period crosses
a critical value. Applying normal form theory and center manifold theorem, we study
the properties of the bifurcating periodic solutions. The model shows that the adopter
population density achieves its maturity stage faster if the cumulative density of external
influences increases. Several numerical examples confirm our theoretical results.</p>