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Dynamical systems with several equilibria and natural Liapunov functions

Vladimir Răsvan (1998)

Archivum Mathematicum

Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines, chemical reactions, economics, biology, neural networks. As pointed out by many researchers, good results on qualitative behaviour of such systems may be obtained if a Liapunov function is available. Fortunately for almost all systems cited above the Liapunov function is associated in a natural way as an energy of a certain kind and it is at least nonincreasing along systems solutions....

Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation

Zhen Wang, Wei Sun, Zhouchao Wei, Xiaojian Xi (2014)

Kybernetika

Hopf bifurcation, dynamics at infinity and robust modified function projective synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were studied in this paper. By using the method of projection for center manifold computation, the subcritical and the supercritical Hopf bifurcation were analyzed and obtained. Then, in accordance with the Poincare compactification of polynomial vector field in $R^{3}$ , the dynamical behaviors at infinity were described completely. Moreover, a...

Dynamics of a class of uncertain nonlinear systems under flow-invariance constraints.

Pastravanu, Octavian, Voicu, Mihail (2003)

International Journal of Mathematics and Mathematical Sciences

Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses.

Huo, Hai-Feng, Li, Wan-Tong (2006)

Discrete Dynamics in Nature and Society

Dynamics of a non-autonomous three-dimensional population system.

Quang, Ta Hong, Ton, Ta Viet, Linh, Nguyen Thi Hoai (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Dynamics of a system of nonlinear differential equations.

Chumakov, G.A. (2007)

Sibirskij Matematicheskij Zhurnal

Dynamics of polynomial systems at infinity.

Kappos, Efthimios (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Dynamics of species in a nonautonomous Lotka-Volterra system.

Ton, Ta Viet (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Dynamics of systems with Preisach memory near equilibria

Stephen McCarthy, Dmitrii Rachinskii (2014)

Mathematica Bohemica

We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...

Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria

D. Okuonghae, A. Korobeinikov (2010)

Mathematical Modelling of Natural Phenomena

This paper presents mathematical models for tuberculosis and its dynamics under the implementation of the direct observation therapy strategy (DOTS) in Nigeria. The models establish conditions for the eradication of tuberculosis in Nigeria based on the fraction of detected infectious individuals placed under DOTS for treatment. Both numerical and qualitative analysis of the models were carried out and the effect of the fraction of detected cases of active TB on the various epidemiological classes...

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