Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems

Applied Mathematics Letters

Volumn 18, Issue 7, 2005, Pages 769-774

  Dimitrov, Dobromir T ^a   Kojouharov, Hristo V ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Dynamical systems; Finite difference; Nonstandard scheme

Indexed keywords

APPROXIMATION THEORY; FINITE DIFFERENCE METHOD; FUNCTIONS; MATHEMATICAL MODELS; RUNGE KUTTA METHODS; THEOREM PROVING;

DISCRETIZATIONS; NONSTANDARD FINITE DIFFERENCE SCHEMES; STABILITY PROPERTIES; TWO DIMENSIONAL AUTONOMOUS DYNAMICAL SYSTEMS;

SYSTEMS ANALYSIS;

EID: 18144420842     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2004.08.011     Document Type: Article

References (12)

1. R.E. Mickens Nonstandard Finite Difference Model of Differential Equations 1994 World Scientific Singapore
2. R. Anguelov, and J.M.-S. Lubuma Contributions to the mathematics of the nonstandard finite difference method and applications Numer. Methods Partial Differential Equations 17 5 2001 518 543
3. A.J. Lotka Elements of Physical Biology 1925 Williams and Wilkins Baltimore
4. R.E. Mickens A nonstandard finite-difference scheme for the Lotka-Volterra system Appl. Numer. Math. 45 2003 309 314
5. R.M. May Stability and Complexity in Model Ecosystem 1974 Princeton University Press Princeton
6. Y. Kuang, and E. Beretta Global qualitative analysis of a ratio-dependent predator-prey system J. Math. Biol. 36 1998 389 406
7. S.-B. Hsu, T.-W. Hwang, and Y. Kuang Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system J. Math. Biol. 42 2001 489 506
8. W. Piyawong, E.H. Twizell, and A.B. Gumel An unconditionally convergent finite-difference scheme for the SIR model Appl. Math. Comput. 146 2003 611 625
9. A.B. Gumel, E.H. Twizell, and P. Yu Numerical and bifurcation analyses for a population model of HIV chemotherapy Math. Comput. Simulation 54 1-3 2000 169 181
10. A.H. Taylor, J.R.W. Harris, J. Aiken, The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification, Mar. Int. Ecohyrd. (J.C. Nihoul (Ed.)) 42 (1986) 313-330
11. S.R.-J. Jang, and L.J.S. Allen A simple food chain with a growth inhibiting nutrient Appl. Math. Comput. 104 1999 277 298
12. D.T. Dimitrov, and H.V. Kojouharov Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response Appl. Math. Comput. 162 2 2005 523 538