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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.

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  • 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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    Cited by:

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    3. 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.
    4. 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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