Differential Equations

Wolfgang Eichhorn and Winfried Gleißner
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Wolfgang Eichhorn: Karlsruhe Institute of Technology (KIT)
Winfried Gleißner: University of Applied Sciences Landshut

Chapter 11 in Mathematics and Methodology for Economics, 2016, pp 535-563 from Springer

Abstract: Abstract In this chapter we deal with differential equations. After defining differential equations we proceed with first order linear differential equations but we also discuss some nonlinear important examples: the Bernoulli and the Riccati equations. The latter is used to investigate the saturation of markets, the logistic growth. As linear differential equations of second order are very important in mathematical modelling they are discussed in full detail. At last we deal with a ubiquitous model in economics and biology the predator-prey model and the Lotka-Volterra differential equations, whose solutions are based on the Poincaré-Bendixson theorem.

Date: 2016
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DOI: 10.1007/978-3-319-23353-6_11

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