Semi-Kolmogorov models for predation with indirect effects in random environments

Tomás Caraballo; Renato  Colucci; Xiaoying Han

doi:10.3934/dcdsb.2016040

Article Contents

2016, Volume 21, Issue 7: 2129-2143. Doi: 10.3934/dcdsb.2016040

This issue Previous Article Analysis of stochastic vector-host epidemic model with direct transmission Next Article Stochastic models in biology and the invariance problem

Semi-Kolmogorov models for predation with indirect effects in random environments

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080 Sevilla
3.
221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849

Received: September 2015

Revised: February 2016

Published: September 2016

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Abstract

In this work we study semi-Kolmogorov models for predation with both the carrying capacities and the indirect effects varying with respect to randomly fluctuating environments. In particular, we consider one random semi-Kolmogorov system involving random and essentially bounded parameters, and one stochastic semi-Kolmogorov system involving white noise and stochastic parameters defined upon a continuous-time Markov chain. For both systems we investigate the existence and uniqueness of solutions, as well as positiveness and boundedness of solutions. For the random semi-Kolmogorov system we also obtain sufficient conditions for the existence of a global random attractor.

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Mathematics Subject Classification: Primary: 92D25; Secondary: 34C60.

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