Continuous Dynamical Systems

  • Glenn Ledder
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


This chapter uses the ideas of continuous dynamics of single populations from Chapter 5 and the techniques of matrix algebra from Chapter 6 to develop the mathematics of continuous dynamical systems. Only autonomous systems are considered. After two sections that introduce a lead poisoning model and Michaelis–Menten kinetics as examples and study them with a combination of nondimensionalization and asymptotic ideas, the heart of the chapter consists of a section on nullcline analysis and two sections on linearized stability analysis. The problem sets consist largely of case studies for models in epidemiology, ecology, environmental science, and physiology, broken into components to fit into the various sections. The chapter concludes with a finished case study that presents a well-known model for HIV interaction with the immune system and uses methods from the chapter to analyze and improve the model.


Equilibrium Point Phase Portrait Equilibrium Solution Solution Curve Forward Reaction 
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Glenn Ledder
    • 1
  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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