Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

We investigate global dynamics of the following systems of difference equations xn+1=xn/A1+B1xn+C1yn, yn+1=yn2/A2+B2xn+C2yn2, n=0,1,…, where the parameters A1, A2, B1, B2, C1, and C2 are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. This system is a version...

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Veröffentlicht in:Abstract and Applied Analysis 2017, Vol.2017 (2017), p.1-19-005
Hauptverfasser: Hadžiabdić, V., Pilav, E., Kulenovic, Mustafa R. S.
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Bifurcation theory
Bifurcations
Biology
Competition
Difference equations
Dynamical systems
Equations, Quadratic
Equilibrium
Geometry
Initial conditions
Mathematical research
Ordinary differential equations
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Beschreibung
Zusammenfassung:We investigate global dynamics of the following systems of difference equations xn+1=xn/A1+B1xn+C1yn, yn+1=yn2/A2+B2xn+C2yn2, n=0,1,…, where the parameters A1, A2, B1, B2, C1, and C2 are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.
ISSN:1085-3375
1687-0409
DOI:10.1155/2017/3104512