
Scientific paper ID 1254 : 2015/3
A CRITERION FOR THE PRESENCE OF A CHAOTIC PROCESS IN 3DIMENSION NONLINEAR DYNAMICAL SYSTEM BY AN ASSESSMENT OF THE ENERGY STATE
Galina Cherneva, Elena Dimkina Mathematical model of continuous nonlinear dynamic system (NDS) is a system of nonlinear differential equations. The number of equations, respectively the number of phase variables in them, defined the dimension of the NDS. It be proved that in order to monitor the promiscuous mode, the system must be least threedimension.
The theory of differential equations is known that a system of three differential equations of first order with three variables can be presented as an inhomogeneous differential equation of one variable of the second degree.On the basis of this presentation are derived generalized expressions of dissipative and free member of the equation as a measure of the energy state of the system. They are used as a criterion for the occurrence of chaotic mode in the system. The proposed criterias are applied to nonlinear circuit described not autonomous equation of Duffing. This equation is a model for many circuits whose a nonlinear element is described by a nonlinear function of the third order. нелинейни динамични системи хаотичен режим дисипация уравнение на Дюфингnonlinear dynamic systems chaotic process dissipation Duffing equationGalina Cherneva Elena Dimkina BIBLIOGRAPHY [1] Matsumoto T., Chua L.O. Journal of circuits, systems and computers. Special Issue on Chua.s Circuit: Paradigm for Chaos. 1993. V. 3(2). [2]Guckenheimer J.M., P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. N.Y. SpringerVerlag,2006. [3] Filipov E., Nelineyna elektrotehnika, S.„Tehnika”, 1979. ( [3] Филипов Е., Нелинейна eлектротехника, С.„Техника”, 1979. ) [4] D.W. Jordon and P. Smith. Nonlinear Ordinary Differential Equation. N.Y. Oxford University Press.1987 [5] I. N. Tabahnev, N. Petkova, Sn. Terzieva, S. Vladov, V. M. Mladenov, “Modeling, Simulations and Implementation of the Chua’s Circuit”, Proceedings of the IVth International Conference on Challenges in Higher Education and Research in the 21 Century, Heron Press Ltd., Vol. 4 pp. 277279, Sozopol, May 31  June 3, 2006, Bulgaria, 