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Mathematical Models of Biological Populations

In: Mathematical Modeling in Economics, Ecology and the Environment

Author

Listed:
  • Natali Hritonenko

    (Prairie View A&M University)

  • Yuri Yatsenko

    (Houston Baptist University)

Abstract

The study of development and interaction of biological species is an important direction of modern research. As one of the central parts of this study, mathematical modeling assists in understanding the behavior of populations and provides reliable forecasts and recommendations for sustainable policies and management. A variety of mathematical models of biological populations and their investigation techniques have been developed, but practice requires new models that consider, for instance, aftereffect and joint influence of different exogenous and endogenous factors. This chapter explores well-known population models that have become a foundation to contemporary models widely used in practice. Section 6.1 presents population models based on ordinary differential equations and basic elements of their analysis. Section 6.2 explores different types of interaction among species and offers a detailed analysis of predator–prey models. Section 6.3 discusses partial differential and integral models of population dynamics.

Suggested Citation

  • Natali Hritonenko & Yuri Yatsenko, 2013. "Mathematical Models of Biological Populations," Springer Optimization and Its Applications, in: Mathematical Modeling in Economics, Ecology and the Environment, edition 2, chapter 0, pages 133-156, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-9311-2_6
    DOI: 10.1007/978-1-4614-9311-2_6
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