Displaying similar documents to “Smooth implications on a finite chain”

On strong chain recurrence for maps

Katsuya Yokoi (2015)

Annales Polonici Mathematici

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This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence...

Embeddings of chains into chains

Vítězslav Novák, Tomáš Novotný (2005)

Discussiones Mathematicae - General Algebra and Applications

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Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.

Possibly Longest Food Chain: Analysis of a Mathematical Model

T. Matsuoka, H. Seno (2008)

Mathematical Modelling of Natural Phenomena

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We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific...