Useful Takeaway: The pitchfork bifiurcation has an "evil twin" -- the subcritical pitchfork happens when an unstable equilibrium splits into a symmetric ... When you have a more complicated 1-D continuous-time system, you can plot the equilibria versus the parameter and look for ...

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The pitchfork bifiurcation has an "evil twin" -- the subcritical pitchfork happens when an unstable equilibrium splits into a symmetric ... This surface represent the equilibria in a 2-parameter family of 1-d systems modeled by the previous spring-disc system.

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So, past the supercritical pitchfork, what determines which way the system buckles? When you have a more complicated 1-D continuous-time system, you can plot the equilibria versus the parameter and look for ...

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  • When you have a more complicated 1-D continuous-time system, you can plot the equilibria versus the parameter and look for ...
  • So, past the supercritical pitchfork, what determines which way the system buckles?
  • This surface represent the equilibria in a 2-parameter family of 1-d systems modeled by the previous spring-disc system.
  • The pitchfork bifiurcation has an "evil twin" -- the subcritical pitchfork happens when an unstable equilibrium splits into a symmetric ...

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Visual Context Gallery

AppDynSys : Bifurcation Examples : Cusp Unfolding
AppDynSys : Bifurcation Examples : Torqued Pendulum
AppDynSys : Bifurcation Examples : Zee Macheen
AppDynSys : Bifurcation Examples : Symmetry & Buckling
AppDynSys : Bifurcation Diagrams : Supercritical Pitchfork
AppDynSys : Bifurcation Examples : Switch
AppDynSys : Bifurcation Diagrams : Subcritical Pitchfork
AppDynSys : Bifurcation Diagrams : Local Analysis
ADS : Vol 1 : Chapter 8.5 : The Cusp & Pitchfork
AppDynSys : Bifurcation Diagrams : Transcritical
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AppDynSys : Bifurcation Examples : Cusp Unfolding

AppDynSys : Bifurcation Examples : Cusp Unfolding

This surface represent the equilibria in a 2-parameter family of 1-d systems modeled by the previous spring-disc system.

AppDynSys : Bifurcation Examples : Torqued Pendulum

AppDynSys : Bifurcation Examples : Torqued Pendulum

Read more details and related context about AppDynSys : Bifurcation Examples : Torqued Pendulum.

AppDynSys : Bifurcation Examples : Zee Macheen

AppDynSys : Bifurcation Examples : Zee Macheen

Read more details and related context about AppDynSys : Bifurcation Examples : Zee Macheen.

AppDynSys : Bifurcation Examples : Symmetry & Buckling

AppDynSys : Bifurcation Examples : Symmetry & Buckling

So, past the supercritical pitchfork, what determines which way the system buckles? Chance. The smallest change in the initial ...

AppDynSys : Bifurcation Diagrams : Supercritical Pitchfork

AppDynSys : Bifurcation Diagrams : Supercritical Pitchfork

Read more details and related context about AppDynSys : Bifurcation Diagrams : Supercritical Pitchfork.

AppDynSys : Bifurcation Examples : Switch

AppDynSys : Bifurcation Examples : Switch

Read more details and related context about AppDynSys : Bifurcation Examples : Switch.

AppDynSys : Bifurcation Diagrams : Subcritical Pitchfork

AppDynSys : Bifurcation Diagrams : Subcritical Pitchfork

The pitchfork bifiurcation has an "evil twin" -- the subcritical pitchfork happens when an unstable equilibrium splits into a symmetric ...

AppDynSys : Bifurcation Diagrams : Local Analysis

AppDynSys : Bifurcation Diagrams : Local Analysis

When you have a more complicated 1-D continuous-time system, you can plot the equilibria versus the parameter and look for ...

ADS : Vol 1 : Chapter 8.5 : The Cusp & Pitchfork

ADS : Vol 1 : Chapter 8.5 : The Cusp & Pitchfork

Read more details and related context about ADS : Vol 1 : Chapter 8.5 : The Cusp & Pitchfork.

AppDynSys : Bifurcation Diagrams : Transcritical

AppDynSys : Bifurcation Diagrams : Transcritical

Read more details and related context about AppDynSys : Bifurcation Diagrams : Transcritical.