Local dynamics in a Leslie-Gower system model

• Autorzy: Dragomirescu F. I. , Caruntu B. , Georgescu R. M.
• Języki publikacji: EN

Abstrakty

EN

Mathematical ecology or/and biology requires the study of populations that interact. This is the reason for the intensive study of the predator-pray models. A Leslie-Gower model of such type is considered here and the stability properties of its equilibrium points are analyticallyand numerically investigated. Dynamics and bifurcations are deduced. Level curves for corresponding Lyapunov functions for various values of the physical parameters in the parameter space are graphically presented emphasizing the stability regions.

Słowa kluczowe

EN

Lyapunov functions; bifurcation problems; predator-prey model

PL

metody Lapunowa; bifurkacja; model drapieżnik-ofiara

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2011
• Tom: Vol. 34
• Strony: 15--26
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Dragomirescu F. I.

• Dept. of Mathematics, Univ. "Politehnica" of Timisoara

autor

Caruntu B.

• Dept. of Mathematics, Univ. "Politehnica" of Timisoara

autor

Georgescu R. M.

• Dept. of Math., Univ. of Pitesti

Bibliografia

• [1] Aeyels, D., Asymptotic stability of nonautonomous systems by Liapunov's direct method, Systems&Control Letters, 25(1995), 273-280.
• [2] Aziz Alaoui, M. A., Study of a Leslie-Gower-type tritrophic population, Chaos, Solitons& Fractals,14 (8), 2002, 1275-1293.
• [3] Arrowsmith, D. K., Place, C.M., Ordinary differential equations, Chapman and Hall, London, 1982.
• [4] Dubey, B., Das, B., Hussain, J., A predator-prey interaction model with self andcross-diffusion, Ecol. Model., 141(2001), 67-76.
• [5] Gatto, M., Rinaldi, S., Stability analysis of predator-prey models via the Liapunov method, Bull. Math. Biology, 39, 1977, 339-347.
• [6] Georgescu, A., Moroianu, M., Oprea, I., Bifurcation theory. Principles and applications, Ed. Univ. Pitesti, Pitesti, 1999. (in Romanian).
• [7] Georgescu, R. M., Georgescu, A., Some results on the dynamics generated by the Bazykin model, Atti dell'Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche, Mathematicae e Naturali, LXXXIV, C1A0601003 (2006), 1-10.
• [8] Georgescu, R. M., Further results on dynamics generated by Bazykin model, Sci. Ann. of Univ. ASVM "Ion Ionescu de la Brad", Iasi, Tom XLVIII 2, 2005, 159-167.
• [9] Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems and bifurcation of vector fields, Appl. Math. Sci., 42, Springer, Berlin, 1983.
• [10] Gunog, S., Kot, M., A comparison of two predator-prey models with Holling's type I functional response, Math. BioSci., 212, 2008, 161-179.
• [11] Ives, A. R., Gross, K., Jansen, V. A. A., Periodic mortality events in predator-prey systems, SIAM J. Appl. Math., 55, 1995, 763-783.
• [12] Kar, T. K., Stability analysis of a prey-predator model incorporating a prey refuge, Communications in Nonlinear Science and Numerical Simulation, 10(2005), 681-691.
• [13] LaSalle, J., Lefschetz, S., Stability by Lyapunov's direct method, Academic Press, New York, 1961.
• [14] Leslie, P. H., Some further notes on the use of matrices in population mathematics, Biometrika, 35, 1948, 213-245.
• [15] Leslie, P. H., A stochastic model for studying the properties of certain biological systems by numerical methods, Biometrika, 45, 1958, 16-31.
• [16] Metzker, K. D., Mitsch, W.J., Modelling self-design of the aquatic community in a newly created freshwater wetland, Ecol. Model., 100 (1997), 61-86.
• [17] Rai, V., Chaos in natural populations: edge or wedge?, Ecological complexity, 1, (2004), 127-138.
• [18] Rinaldi, S., Muratoni, S., Kuznetsov, S., Multiple attractors catastrophes and chaoes in seasonally perturbed predator-prey communities, Bull. Math. Biol., 55, (1993), 15-35.
• [19] Vincent, T. L., Grantham, W. J., Nonlinear and optimal control systems, J. Wiley, 1997.
• [20] Upadhayay, R. K., Iyengar, S. R. K., Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems, Nonlinear Analysis: Real World Applications, 6, (2005), 509-530.