Dynamical analysis of an innovation diffusion model with evaluation period

  • Rakesh Kumar S.B.S. State Technical Campus Department of Applied Sciences
  • Anuj Kumar Sharma L.R.D.A.V. College, Jagraon Department of Mathematics
  • Kulbhushan Agnihotri S.B.S. State Technical Campus, Ferozepur Department of Applied Sciences

Resumen

A nonlinear form of innovation diffusion model consisting of two driving equations governed by two variables namely adopter and non-adopter population density is proposed to lay stress on the evaluation period. The model is analyzed qualitatively with stability theory, Hopf-bifurcation analysis by taking evaluation period as a control parameter to see the role of evaluation period in shaping the dynamics of adopter and non-adopters. The threshold value of evaluation period is determined beyond which small amplitude oscillations of adopter and non-adopter population occur and goes on decreasing with the increase in carrying capacity of non-adopter class. The sensitivity analysis of the state variables w.r.t. the model parameters is performed at a non-zero equilibrium point. The effect of external influences to achieve maturity stage is also discussed. The analytical results so obtained are verified through numerical simulations by using the Matlab software.

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Biografía del autor/a

Rakesh Kumar, S.B.S. State Technical Campus Department of Applied Sciences
Assistant Professor, Department of Applied Sciences,
Anuj Kumar Sharma, L.R.D.A.V. College, Jagraon Department of Mathematics
Associate Professor, Department of Mathematics
Kulbhushan Agnihotri, S.B.S. State Technical Campus, Ferozepur Department of Applied Sciences
Associate Professor, Department of Applied Sciences
Publicado
2019-03-31
Sección
Articles