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Kamran Bigdely
Kamran Bigdely
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Suppose we have a dynamical system

$\dot{x} = f(x,r)$

in which x is a state variable and r is a bifurcation parameter. How to figure out which kind of bifurcation(s) (e.g. saddle-node, transcritical, pitchfork, hopf and etc) the system undergoes?

Edit 1: consider the space as 1D or 2D.

Suppose we have a dynamical system

$\dot{x} = f(x,r)$

in which x is a state variable and r is a bifurcation parameter. How to figure out which kind of bifurcation(s) (e.g. saddle-node, transcritical, pitchfork, hopf and etc) the system undergoes?

Suppose we have a dynamical system

$\dot{x} = f(x,r)$

in which x is a state variable and r is a bifurcation parameter. How to figure out which kind of bifurcation(s) (e.g. saddle-node, transcritical, pitchfork, hopf and etc) the system undergoes?

Edit 1: consider the space as 1D or 2D.

Source Link
Kamran Bigdely
Kamran Bigdely
  • 201
  • 1
  • 4
  • 9

How to figure out the type of the bifurcation in a dynamical system?

Suppose we have a dynamical system

$\dot{x} = f(x,r)$

in which x is a state variable and r is a bifurcation parameter. How to figure out which kind of bifurcation(s) (e.g. saddle-node, transcritical, pitchfork, hopf and etc) the system undergoes?