Bifurcation Theory and Bistability

  • Hamid Reza NooriEmail author
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


In this chapter, we will recapitulate the essential concepts, definitions and theorems of the Lyapunov and Andronov stability theories of dynamical systems. The global aim is to prepare the reader for the mathematical abstraction of biological switches and hysteresis phenomena. Furthermore, the expected readership, which are students and researchers interested in mathematical modeling of biological processes, will benefit in general from this chapter since it provides the essence of stability of dynamical systems in a brief and precise way.


Vector Field Periodic Orbit Equilibrium Point Stable Manifold Bifurcation Theory 
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  1. Kotus J, Kyrch M, Nitecki Z (1982) Global structural stability of flows on open surfaces. Mem Am Math Soc 37:1–108Google Scholar
  2. Peixoto M (1962) Structural stability on two-dimensional manifolds. Topology 1:101–120MathSciNetCrossRefzbMATHGoogle Scholar
  3. Perko L (2008) Differential equations and dynamical systems. Springer, HeidelbergGoogle Scholar
  4. Verhulst F (2008) Nonlinear differential equations and dynamical systems. Springer, HeidelbergGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Central Institute for Mental HealthInstitute for PsychopharmacologyMannheimGermany

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