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

By Elsayed Mohamed Elsayed Ahmed, Ahmed M. A. El-Sayed, Hala A. A. El-Saka. 2007

718 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/bc8d782e9ef3904c44535f94dab9161014501862

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In Geometry and Topology

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Citations in the corpus

A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators (2020, background): “…various types of predator–prey models have been perused by many authors such as Kumar et al. [54, 55], Ghanbari et al. [56–59], Huang et al. [60], Alidousti et al. [61], Zhou et al. [62], Wang et al. [63], Das et al. [64], Li et al. [65], Ghaziani et al. [66], Ahmed et al. [67] and Yu et al. [68].”
Adaptive feedback control and synchronization of non-identical chaotic fractional order systems (2010, background): “Fractional order systems are at least as stable as their integer order counterpart, because systems with memory are typically more stable than their memory-less counterpart [ 40 ].”
On asymptotic properties of solutions to fractional differential equations (2018, methodology): “The first work concerning with Lyapunov’s first method for fractionalorder systems is the paper [3].”
Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization (2014, methodology): “For these reasons, FOD have been successfully applied in mathematical biology [5–7] and some other interdisciplinary fields [8–11].”
On the fractional-order logistic equation (2007, result): “It must be noted that these results are the same results as for studying the stability of the initial value problem of the ordinary differential equation Also these results agree with [2,3,17].”
A Fractional Order SEIR Model with Density Dependent Death Rate ABSTRACT | FULL TEXT (2011, background): “In recent years, it has turned out that many phenomena in different fields can be described very successfully by the models using fractional order differential equations [1,2,4,6].”