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Effects of competition and predation in a three species model

Janusz Szwabiński, Andrzej Pękalski, Kamil Trojan (2008)

Banach Center Publications

A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.

Eight-shaped Lissajous orbits in the Earth-Moon system

Grégory Archambeau, Philippe Augros, Emmanuel Trélat (2011)

MathematicS In Action

Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) L 1 , ... , L 5 . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [20, 21, 22, 23, 37]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...

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