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Fig. 2 | SpringerPlus

Fig. 2

From: Competition for resources: complicated dynamics in the simple Tilman model

Fig. 2

Numerical solution of a system of a single consumer B and a single resource R (parameter values, specified in the text, are such that there is stable coexistence of consumer and resource). Initially the resource is absent and the consumer density is small. The time plot a shows that the resource rapidly grows to its stable level, while the consumer density remains small. When the latter increases, the resource density drops, and both densities relax to the coexistence equilibrium level. The phase plot b shows the trajectory as produced by the consecutive states of the numerical iteration procedure with fixed time step, the marker points. The system moves rapidly from the initial state, indicated by the red dot, to the trivial equilibrium, a saddle point, and next moves directly to the stable coexistence point. Next the parameters are modified to create a substantial difference in time scales between the growth rates of the resource and the consumer. The time plot c shows that in the final relaxation both densities show oscillating behaviour. Again the phase plot d shows that the system first moves to the unstable trivial equilibrium, but now spirals into the stable coexistence point

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