SPECTRAL PROPERTIES OF LOTKA VOLTERRA DYNAMIC SYSTEMS

Authors

  • Sarvinoz Maqsimova Doctorate student of the Mathematics faculty, Andijan State University, Andijan, Uzbekistan.

DOI:

https://doi.org/10.55640/

Keywords:

Lotka--Volterra map; homogeneous tournament; fixed point; Jacobian spectrum;

Abstract

We study the spectral properties of Jacobians at fixed points in discrete Lotka--Volterra maps associated with two types of homogeneous tournaments. We used python scipt to classify 3--support and compute their spectra when $a_{ki}=\pm 1$. Our results reveal general eigenvalue patterns, independent of the tournament size, with applications to stability and structural dynamics of systems.

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References

1. Ganikhodzhaev R.N. A chart of fixed points and Lyapunov functions for a class of discrete dynamical systems, Math. Notes, 56 (5-6), (1994) pp.1125-1131.

2. Ganikhodzhaev R.N. Quadratic stochastic operators, Lyapunov function and tournaments, Acad. Sci. Sb. Math., 76(2), p. 489-506. (1993)

3. Ganikhodzhaev R.N., Tadzhieva M.A. Stability of fixed points of discrete dynamic systems of Volterra type. AIP Conference Proceedings, 2021. V. 2365. P. 060005-1 $-$ 060005-7. https://doi.org/10.1063/5.0057979. (Scopus. IF=0.7).

4. Kh. Koh and F. Dong and E.G. Tay. Introduction to graph theory. World Scientific. p. 308. (2024)

5. Moon,J.~W. Topics on Tournaments, New York: Holt, {it Rinehart and Winston}, 1968, p. 112.

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Published

2025-12-13

Issue

Vol. 4 No. 11 (2025): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

SPECTRAL PROPERTIES OF LOTKA VOLTERRA DYNAMIC SYSTEMS. (2025). Journal of Multidisciplinary Sciences and Innovations, 4(11), 1503-1507. https://doi.org/10.55640/

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