Basic stage structure measure valued evolutionary game model

John Cleveland

doi:10.3934/mbe.2015.12.291

Article Contents

2015, Volume 12, Issue 2: 291-310. Doi: 10.3934/mbe.2015.12.291 open access

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Basic stage structure measure valued evolutionary game model

John Cleveland^1,

1.
University of Wisconsin-Richland, 1200 Hwy 14 West, Richland Center, WI 53581-1399

Received: March 31, 2014

Revised: August 31, 2014

Published: November 2014

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Abstract

The ideas and techniques developed in [12,3] are extended to a basic stage structured model. Each strategy consists of two stages: a Juvenile (L for larvae), and Adult (A). A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures. Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. Similar to [12] we also have the unifying of discrete and continuous systems and the containment of the classic nonlinearities.

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Mathematics Subject Classification: Primary: 91A22, 34G20, 37C25, 92D25.

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