DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

doi:10.1007/s10473-022-0120-1

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 364-386.doi: 10.1007/s10473-022-0120-1

DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

Rakesh KUMAR¹, Anuj Kumar SHARMA², Govind Prasad SAHU³

1. Department of Applied Sciences, Shaheed Bhagat Singh State University, Ferozepur, Punjab, 152004, India;
2. Department of Mathematics, L.R.D.A.V. College, Jagraon, Ludhiana, Punjab, 142026, India;
3. Center for Basic Sciences, Pt Ravishankar Shukla University, Raipur (Chhattisgarh), India

收稿日期:2020-05-29 修回日期:2020-11-09 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Rakesh KUMAR,E-mail:keshav20070@gmail.com E-mail:keshav20070@gmail.com
作者简介:Anuj Kumar SHARMA,E-mail:anujksuma1968@gmail.com;Govind Prasad SAHU,E-mail:govind3012@gmail.com

DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

Rakesh KUMAR¹, Anuj Kumar SHARMA², Govind Prasad SAHU³

1. Department of Applied Sciences, Shaheed Bhagat Singh State University, Ferozepur, Punjab, 152004, India;
2. Department of Mathematics, L.R.D.A.V. College, Jagraon, Ludhiana, Punjab, 142026, India;
3. Center for Basic Sciences, Pt Ravishankar Shukla University, Raipur (Chhattisgarh), India

Received:2020-05-29 Revised:2020-11-09 Online:2022-02-25 Published:2022-02-24
Contact: Rakesh KUMAR,E-mail:keshav20070@gmail.com E-mail:keshav20070@gmail.com

摘要/Abstract

摘要： In this paper, we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation (product) in a particular region. The model exhibits two equilibria, namely, the adopter-free and an interior equilibrium. The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number (BIN) R_A. It is investigated that the adopter free steady-state is stable if R_A < 1. By considering τ (the adoption experience of the adopters) as the bifurcation parameter, we have been able to obtain the critical value of τ responsible for the periodic solutions due to Hopf bifurcation. The direction and stability analysis of bifurcating periodic solutions has been performed by using the arguments of normal form theory and the center manifold theorem. Exhaustive numerical simulations in the support of analytical results have been presented.

关键词: intra-specific competition, basic influence number, local stability, Hopf-bifurcation, normal form theory, center manifold theorem

Abstract: In this paper, we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation (product) in a particular region. The model exhibits two equilibria, namely, the adopter-free and an interior equilibrium. The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number (BIN) R_A. It is investigated that the adopter free steady-state is stable if R_A < 1. By considering τ (the adoption experience of the adopters) as the bifurcation parameter, we have been able to obtain the critical value of τ responsible for the periodic solutions due to Hopf bifurcation. The direction and stability analysis of bifurcating periodic solutions has been performed by using the arguments of normal form theory and the center manifold theorem. Exhaustive numerical simulations in the support of analytical results have been presented.

Key words: intra-specific competition, basic influence number, local stability, Hopf-bifurcation, normal form theory, center manifold theorem

中图分类号:

34C23

Rakesh KUMAR, Anuj Kumar SHARMA, Govind Prasad SAHU. DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS[J]. 数学物理学报(英文版), 2022, 42(1): 364-386.

Rakesh KUMAR, Anuj Kumar SHARMA, Govind Prasad SAHU. DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS[J]. Acta mathematica scientia,Series B, 2022, 42(1): 364-386.

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DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

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