Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models

In this paper we are concerned with the fractional-order predator–prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibr...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2007, Vol.325 (1), p.542-553
Main Authors: Ahmed, E., El-Sayed, A.M.A., El-Saka, H.A.A.
Format: Article
Language:English
Subjects:
Equilibrium points
Exact sciences and technology
Existence and uniqueness
Fractional-order differential equations
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Numerical solution
Ordinary differential equations
Predator–prey system
Predictor–corrector method
Rabies system
Sciences and techniques of general use
Stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper we are concerned with the fractional-order predator–prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.01.087