Dynamics of Some Three-Dimensional Lotka–Volterra Systems

Abstract

We characterize the dynamics of the following two Lotka–Volterra differential systems: $$\begin{aligned} \begin{array}{lll} \dot{x}=x(r+a y+b &{} &{} \dot{x}=x(r+ax+b y+c z), \dot{y}=y(r-a x+c &{} \quad \text{ and }\quad \quad &{} \dot{y}=y(r+a x+dy+e z), \dot{z}=z(r-b x-c y), &{} &{} \dot{z}=z(r+a x+d y+fz). \end{array} \end{aligned}$$ We analyze the biological meaning of the dynamics of these Lotka–Volterra systems