Displaying similar documents to “The population dynamics of conflict and cooperation.”

Local Collapses in the Truscott-Brindley Model

I. Siekmann, H. Malchow (2008)

Mathematical Modelling of Natural Phenomena

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Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses...

On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles

R. Dilão, A. Lakmeche (2010)

Mathematical Modelling of Natural Phenomena

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We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient...

Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno (2010)

Mathematical Modelling of Natural Phenomena

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With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the...