Choque Rivero, Abdon Eddy | Universidad Michoacana De San Nicolas De Hidalgo |
Rico-Melgoza, J. Jesus | Universidad Michoacana De San Nicolas De Hidalgo |
Ornelas-Tellez, Fernando | Universidad Michoacana De San Nicolas De Hidalgo |
Resumen: This paper deals with the solution of achieving finite-time stabilization for a Leslie-Gower prey-predator system through a bounded control input. Simulation results show the effectiveness of the proposed control methodology.
Total descargados hasta ahora
143 Downloads
¿Cómo citar?
Abdon E. Choque-Rivero, , J. Jesus Rico-Melgoza & Fernando Ornelas-Tellez. Finite Time Stabilization of the Prey Predator Model. Memorias del Congreso Nacional de Control Automático, pp. 395-400, 2019.
Palabras clave
Control de Sistemas No Lineales, Procesos Biológicos
Referencias
- Bath S. P., Berstein D. S., “Lyapunov analisis of finitetime differential equations,” Proceeding of the American Control Conference, vol.3, pp.1831–1832, June 1995.
- Choque Rivero A. E. , “The controllability function method for the synthesis problem of a nonlinear control system,” International Review of Automatic Control, vol. 1 no.4, pp. 441-445, 2008.
- Choque Rivero A. E., Korobov V. I., Skoryk V. O., “Controllability function as time of motion. I,” (in Russian) Mat. Fiz. Anal. Geom, vol. 11, no. 2, pp. 208-225, 2004. English translation in http://arxiv.org/abs/1509.05127.
- Choque Rivero A. E., Korobov V. I., Skoryk V. O., “Controllability function as time of motion. II,” (in Russian) Mat. Fiz. Anal. Geom, vol. 11, no. 3, pp. 341- 354, 2004.
- Dorato, P. (1967). Comment on finite-time stability under perturbing forces and on product spaces. IEEE Trans. Automat. Contr. June, pp 340.
- Dorato, P. (2006). An overview of finite-time stability. Current trends in nonlinear systems and control, Systems & Control: Foundations & Applications pp. 185- 194, 2004.
- Collings, J.B. (1997). The effects of the functional response on the bifurcation behavior of a mite predatorprey interaction model. J. Math. Biol., 36, 149–168.
- Gakkhar, S. and Singh, A. (2012). Complex dynamics in a prey predator system with multiple delays. Commun. Nonlinear Sci. Num. Simul., 17, 914–929.
- Jiang, J. and Song, Y. (2013). Stability and bifurcation analysis of a delayed leslie-gower predator-prey system with nonmonotonic functional response. Hindawi Publishing Corporation, 2013, 19 pages.
- Kamenkov G., “ On stability of motion over a finite interval of time,” Journal of Applied Math. and Mechanics (PMM) 18:512.
- Korobov V. I., “A general approach to the solution of the problem of synthesizing bounded controls in a control problem,” Mat. Sb. vol. 109, no. 151, pp. 582-606, 1979 (in Russian). English transl.: Mat. Sb. vol. 37, no. 4, pp. 535-557, 1980.
- Lasalle, J. and Letfschetz, S. (1961). Stability by Liapunov’s direct method. Academic Press, New York.
- Leslie, P. and Gower, J. (1960). The properties of a stochastic model for the predator-prey type of interaction between two species. Biometrica, 47, 219–234.
- Li, Y. and Xiao, D. (2007). Bifurcations of a predatorprey system of holling and leslie types. Chaos Solitons and Fractals, 34, 606–620.
- Pielou, E. (1969). An introduction to mathematical ecology. New York: Wiley-Interscience, New York, NY, USA.
- Poznyak A. S., Polyakov A. Ye., Strygin V.V., “Analysis of finite-time convergence by the method of Lyapunov functions in systems with second-order sliding modes”, J. Appl. Math. Mech, vol.75, pp. 289-303, 2011.
- Singh, A., Stabilization of prey predator model via feedback control. Applied Analysis in Biological and Physical Sciencies, Springer Proceedings in Mathematics & Statistics 186, 2016, DOI 10.1007/978-81-322-3640- 5_10.
- Weiss, L. and Infante E. F., Finite time stability under perturbing forces and produc spaces IEEE Trans. Automat. Contr., AC-12, No.1, 54–59.