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Bifurcation analysis in the diffusive Lotka–Volterra system: An application to market economy

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  • Wijeratne, A.W.
  • Yi, Fengqi
  • Wei, Junjie

Abstract

A diffusive Lotka–Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.

Suggested Citation

  • Wijeratne, A.W. & Yi, Fengqi & Wei, Junjie, 2009. "Bifurcation analysis in the diffusive Lotka–Volterra system: An application to market economy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 902-911.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:902-911
    DOI: 10.1016/j.chaos.2007.08.043
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    1. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Chaos in a food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 159-166.
    2. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 11(5), pages 895-953, November.
    3. Sanjeev Swami & Pankaj Khairnar, 2006. "Optimal normative policies for marketing of products with limited availability," Annals of Operations Research, Springer, vol. 143(1), pages 107-121, March.
    4. Donald Lehmann & Mercedes Esteban-Bravo, 2006. "When giving some away makes sense to jump-start the diffusion process," Marketing Letters, Springer, vol. 17(4), pages 243-254, December.
    5. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    6. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
    7. Renato Guseo & Alessandra Valle, 2005. "Oil and gas depletion: Diffusion models and forecasting under strategic intervention," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 375-387, December.
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    Cited by:

    1. Hoang-Sa Dang & Ying-Fang Huang & Chia-Nan Wang & Thuy-Mai-Trinh Nguyen, 2016. "An Application of the Short-Term Forecasting with Limited Data in the Healthcare Traveling Industry," Sustainability, MDPI, vol. 8(10), pages 1-14, October.
    2. Yang, Ruizhi & Wei, Junjie, 2015. "Bifurcation analysis of a diffusive predator–prey system with nonconstant death rate and Holling III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 1-13.
    3. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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