nvestigation of the Stability for the Melting Liquid Phase Nanoparticles Model

  • Hero W. Salih Department of mathematics, College of Science, Salahaddin University- Erbil, Kurdistan Region, Iraq.
Keywords: Fluoxetine,Depression,Liver,Kidney,Cerebrum

Abstract

       This work we prfesent the investigate stability of both liquid single phase limit for melting nanoparticle, heating liquid models. For the study we transform both modeles to Lienard equations. The associated Lyapunov function of both models are computed by using the Lyapunov direct method, the stability for both system are established, and these imply that the models are stable under the given initial and boundary conditions. Physically this means that the liquid and heating liquid nanoparticales system are stable in the plane. Finally we investigate the existence of limit cycles for both systems are found to be non-existent

References

CHUA, L.O.,KOMURO,M., MATSUMOTO, T. 1986. The double scroll family. . IEEE T Circuits S-I, 33, 1073-1118.
KENNEDY, M. P.1994. chaos in the Colpits oscillator. . IEEE T Circuits S-I, 41, 771-774.
RAO, MRM. 1981. Ordinary differential equations theory and applications. London, UK: Edward Arnold Ltd.
TCHITINGA, R., FOTSIM, H.B.,NANA, B., FOTSO, P.H.L. WOAFO, P. 2012. Hartley's oscillator: the simplest chaotic two-component circuit. Chaos Soliton Fract, 45, 306-313
UYAROGLU, Y., KOCAMAZ, U.E. 2014. Synchronization of Vilnius chaotic oscillators with active and passive control. J. Circuit Syst. Comp.,23,1-17.
WU, B. 2008.Mathematical modelling of nanoparticale melting or freezing, University of Wollongong .
YANG, C. SUN, J., ZHANG, Q., MA, X. 2013. Lyapunov stability and strong passivity analysis for nonlinear descriptor systems. IEEE T Circuits S-I, 60, 1003-1012.
YE, Y., LO, C. 2009. Theory of Limit Cycles, American Mathematical Society.
ZHANG, L., YU, L. 2013. Global asymptotic stability of certain third- order nonliner differential equations. Math Meth Appl Sci, 36,1845-1850
Published
2019-05-12
How to Cite
Salih, H. “Nvestigation of the Stability for the Melting Liquid Phase Nanoparticles Model”. ZANCO Journal of Pure and Applied Sciences, Vol. 31, no. 2, May 2019, pp. 40-44, doi:10.21271/zjpas.31.s2.5.