Bifurcations in a discretized economic model: analytical and numerical approaches

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran

2 Department of Mathematics, Faculty of Science, Fasa University, Fasa, Iran

Abstract

‎This paper explores a continuous-time economic model and proposes a technique for discretizing it into a discrete-time system using Euler's method‎. ‎By manipulating the parameter $\omega$‎, ‎which represents the savings proportion‎, ‎we determine the critical coefficient of bifurcations in the normal form using the central manifold‎. ‎The coefficient for flip and Neimark-Sacker bifurcations at the trivial fixed point is obtained through affine transformations‎, ‎while closed forms are employed for other types of bifurcations‎. ‎To analyze the conditions and coefficients of the normal forms for each bifurcation‎, ‎we employ both analytical and numerical methods‎. ‎Additionally‎, ‎we visualize the bifurcation curve in the parameter space and generate a bifurcation diagram using the MatcontM package.‎

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References

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Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 07 June 2026

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History

  • Receive Date: 26 December 2025
  • Revise Date: 10 May 2026
  • Accept Date: 06 June 2026

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