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Dynamics of a competitive Lotka-Volterra systems in \(\mathbb{R}^3\). (English) Zbl 1467.34050

Summary: We describe the dynamics of the 3-dimensional competitive Lotka-Volterra systems \[ \dot{x}=x(a-x-y-z),\quad \dot{y}=y(b-x-y-z),\quad \dot{z}=z(c-x-y-z), \] providing the phase portraits for all the values of the parameters \(a,b\) and \(c\) with \(0< a< b< c\) in the positive octant of the Poincaré ball.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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