Delay Induced Hopf Bifurcation in a Nonlinear Innovation Diffusion Model: External Influences Effect

2018 ◽  
Vol 8 (3) ◽  
pp. 422-446
Author(s):  
Rakesh Kumar
2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Rakesh Kumar ◽  
Anuj Kumar Sharma

This article is concerned with the diffusion of a sport in a region, and the innovation diffusion model comprising of population classes, viz. nonadopters class, information class and adopters class. A qualitative analysis is carried out to assess the global asymptotic stability of the interior equilibrium for null delay. It has also been proved that the parameter [Formula: see text] (age gaps among sportspersons) in the intra-specific competition between the new players and the senior players can even destabilize the otherwise globally stable interior equilibrium state and the coexistence of all the populations is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and center manifold arguments, the stability of bifurcating periodic orbits is determined. Numerical simulations have been executed in support of the analytical findings.


2021 ◽  
Vol 12 (3) ◽  
pp. 95
Author(s):  
Weiwei Sun ◽  
Zheng Zhang

Electric vehicle cell industry is an emerging area with fierce competition on technical innovation, in which the patent holder can choose different innovation diffusion options to maximize the return; however, the strategy is unclear in certain scenarios. We tried to explain the question of how to maximize the patent holder’s return by appropriate patent license strategy to promote EV cell innovation diffusion, when competition and patent licensing relationship exist in the supply chain. A multistage and multichannel diffusion model of EV cell comprising the patent holder, EV cell producer and EV producers is developed; the evolutionary game is analyzed considering the competition among same stage players and patent licensing relationship among different stage players; and an optimization algorithm is introduced to find the maximum weighted object function of the patent holder. We established the multistage and multichannel diffusion model and found a nonlinear complex relationship between patent holder object function and the key factors including patent royalty pricing and innovation advantage coefficient; in addition, an optimization algorithm is developed based on adopters’ decision-making related with competition and patent licensing.


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