Elements of Applied Bifurcation Theory¶
Kuznetsov, Y. A. (1995). Elements of Applied Bifurcation Theory. Springer.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Phase Diagram
- Beyond classical thermodynamics, phase diagrams generalize to non-physical systems — economic regimes, biological population steady states, dynamical bifurcation diagrams — wherever qualitatively distinct operating modes are mapped across continuous control-parameter space.
This sourceRigorous analysis of bifurcation diagrams; maps dynamical transitions onto abstract phase diagrams organized by stability and criticality.
Supported in partVerified against the publisher's abstract
The abstract places bifurcation theory and its parameter-varying analysis among modelling tools for physics, biology and economics, backing only the bifurcation-diagram example, not the full phase-diagram generalization.
“It is also addressed to professional researchers in physics, biology, engineering, and economics who use dynamical systems as modeling tools in their studies.”
- Beyond classical thermodynamics, phase diagrams generalize to non-physical systems — economic regimes, biological population steady states, dynamical bifurcation diagrams — wherever qualitatively distinct operating modes are mapped across continuous control-parameter space.
- Tipping Points (or Phase Transitions)
- Bifurcation analysis provides tools for classifying these points
This sourceRigorous analysis of bifurcation diagrams; maps dynamical transitions onto abstract phase diagrams organized by stability and criticality.
- Bifurcation analysis provides tools for classifying these points
Verification¶
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