A Lyapunov Function For Logistic Equation On Time Scales

Year 2018, Volume: 22 Issue: 6 , 1628 - 1630 , 01.12.2018

Veysel Fuat Hatipoğlu

https://doi.org/10.16984/saufenbilder.395615

https://izlik.org/JA94HS72GL

Abstract

In this study we focus on the stability of dynamic logistic equation which is used in single species population dynamics. Here we have introduced a quadratic Lyapunov function for generalized dynamic logistic equation on time scales. By using proposed Lyapunov function, asymptotic stability conditions for the equilibrium solution of dynamic logistic equation have been investigated. 

Keywords

Dynamic logistic equation , Lyapunov Function , Stability , Time Scales

References

• Bohner, M., and Peterson, A. Dynamic Equations on Time Scales: An Introduction With Applications. Springer Science & Business Media, 2001.
• Bohner, M., and Peterson, A. C. (Eds.). Advances in dynamic equations on time scales. Springer Science & Business Media, 2002.
• T. Gard and J. Hoffacker, “Asymptotic behavior of natural growth on time scales,” Dynamic Systems and Applications, vol. 12, no. 1-2, pp. 131–148, 2003.
• Lakshmikantham, V., Sivasundaram, S., and Kaymakcalan, B. Dynamic systems on measure chains (Vol. 370). Springer Science & Business Media, 2013.
• J. Zhang, M. Fan, and H. Zhu, “Periodic solution of single population models on time scales,” Mathematical and Computer Modelling, vol. 52, no. 3, pp. 515–521, 2010.