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The stability of an innovation diffusion model with delay. (Chinese. English summary) Zbl 1051.34061

Summary: An innovation diffusion model with distributed time delay is proposed and its effect on the diffusion process is studied. The existence and uniqueness of a positive equilibrium is proven and sufficient conditions for its locally and globally asymptotic stability are obtained. When the kernel function of the distributed time delay takes the form \(ae^{-a\tau}\), the positive equilibrium is absolutely asymptotically stable.

MSC:

34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
90B99 Operations research and management science
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