A Lyapunov Function For Logistic Equation On Time Scales

ISSN: 1301-4048
Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 1997
Yayıncı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü

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.

PDF

___

[1] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications. Springer Science & Business Media, 2001.

[2] M. Bohner and A. Peterson, Advances in dynamic equations on time scales. Springer Science & Business Media, 2002.

[3] 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.

[4] V. Lakshmikantham, S. Sivasundaram, and B. Kaymakcalan, Dynamic systems on measure chains (Vol. 370). Springer Science & Business Media, 2013.

[5] 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.

[6] P. Cull, “Stability of discrete onedimensional population models,” Bulletin of Mathematical Biology, vol. 50, no. 1, pp. 67- 75, 1988.

[7] M. W. Hirsch, S. Smale, and R. L. Devaney, Differential equations, dynamical systems, and an introduction to chaos. Academic press, 2012.

[8] J. M. Davis, I. A. Gravagne, R. J. Marks, and A.A. Ramos, “Algebraic and dynamic Lyapunov equations on time scales.” In Proc. IEEE 42nd Southeastern Symposium on System Theory (SSST), 2010, pp. 329- 334.