Stability of The Equilibrium of Nonlinear Dynamical Systems

Dzhalladova, Irada A.; Růžičková, Miroslava

doi:10.2478/tmmp-2018-0007

Abstract

The algorithm for estimating the stability domain of zero equilibrium to the system of nonlinear differential equations with a quadratic part and a fractional part is proposed in the article. The second Lyapunov method with quadratic Lyapunov functions is used as a method for studying such systems.

References

[1] BELOZEROV, V. E.—VOLKOV, S. A.: A Geometric Approach to the Stabilization of Control Systems. Ed. of Dnipropetrovsk National University, Dnepropetrovsk, 2006.
Search in Google Scholar Back to article
[2] KHUSAINOV, D. Y.—DZHALLADOVA, I. A.: Evaluation of stability region of differential systems with quadratic right-hand side, Bulletin of Kiev University. Series: Physics and mathematics B.3 (2011), 227–230. (In Russian)
Search in Google Scholar Back to article
[3] KHUSAINOV, D. Y. ET AL.: Linear Dynamical Systems with After-effect. KNU, Kiev, 2015. (In Russian)
Search in Google Scholar Back to article
[4] KHUSAINOV, D. Y.—DAVYDOV, V.: Evaluation of stability region of quadratic differential systems, Bulletin of Kiev University, Series: Physics and mathematics, B. 2, 1991, 3–6. (In Russian)
Search in Google Scholar Back to article
[5] RŮŽIČKOVÁ, M.—KUZMICH, O.—KHUSAINOV, D. Y.: The estimation of the dynamics of indirect control switching systems, Tatra Mt. Math. Publ. 48 (2011), 197–213.10.2478/v10127-011-0018-0
Search in Google Scholar Back to article
[6] KOLMANOVSKII, V. B.: Delay equations and mathematical modelling, Soros Educational Journal 4, (1996), 122–127.
Search in Google Scholar Back to article
[7] KOLMANOVSKII, V. B.—NOSOV, V. R.: Stability and Periodic Modes of Control Systems with After Effect. Nauka, Moscow, 1981. (In Russian)
Search in Google Scholar Back to article
[8] SMITH, J.: Models in Ecology. Mir, Moskow, 1976. (In Russian)
Search in Google Scholar Back to article
[9] ZHANG, W.-B.: Synergetic Economics. Time and Change in Non-linear Economics. Mir, Moskow, 1999. (In Russian)
Search in Google Scholar Back to article

Stability of The Equilibrium of Nonlinear Dynamical Systems

Abstract

Paradigm

My account