In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation, which improves and generalizes some known ones in the existing literature. ...Especially, our results completely solve an open problem and some conjectures proposed in 1, 2, 3, 4.
In this paper a method of approximating the classical LSW model near self-similar solutions for initial data with infinite support is developed. The resulting problem is an integrodifferential ...equation having two time scales that can be studied using multiple scale methods. The analysis provides a detailed description of the precise manner in which the characteristics “leak” through the critical radius associated to the self-similar solutions. The analysis in this paper makes precise the meaning of the iterated logarithmic asymptotics in the dynamics of the LSW model that were already obtained in the original Lifshitz-Slyozov paper. Examples of noncompactly supported solutions of the LSW model that do not behave in a self-similar manner are also given.
This paper describes in a rigorous manner how the dynamics of the characteristic curves for the Lifshitz-Slyozov-Wagner (LSW) model of coarsening transforms a class of noncompactly supported initial ...data in functions that behave in a self-similar manner for long times.
Intermingled basins in a two species system Hofbauer, Franz; Hofbauer, Josef; Raith, Peter ...
Journal of mathematical biology,
09/2004, Letnik:
49, Številka:
3
Journal Article
Recenzirano
We present simple examples of (competitive) two species systems with complicated dynamic behaviour. From almost all initial conditions one of the two species dies out. But the survivor is ...unpredictable: The basins of the two chaotic one-species attractors are everywhere dense and intermingled.
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