Instabilities & Chaos

  • Fritz K. Kneubühl


An oscillation represents a highly regular motion of a physical, chemical, biological or ecological system. This motion can be disturbed by structural changes of the system and become instable or chaotic. On certain conditions a structural change of a system can have a drastic effect on the motion in the form of a bifurcation. This can imply changes of stability, generation of subharmonics by period doubling, new kinds of motion or chaos. Chaos can be produced even by completely deterministic systems. In this chapter these scenarios are discussed with special emphasis on bifurcations and deterministic chaos and exemplified by the continuous Lorenz model and by the discrete logistic map.


Singular Point Lyapunov Exponent Hopf Bifurcation Bifurcation Diagram Bifurcation Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Fritz K. Kneubühl
    • 1
  1. 1.Institute of Quantum Electronics, Physics DepartmentSwiss Federal Institute of Technology (ETH)ZürichSwitzerland

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