A bifurcation diagram is a plot that shows how the equilibrium values of a dynamical system change as a parameter varies. It is constructed by plotting the equilibrium values (z) on the vertical axis against the parameter (C) on the horizontal axis.
Conditions: The system is described by a family of ODEs parameterized by C.; Equilibria are determined for a range of C values.
A bifurcation diagram is a plot that shows how the equilibrium values of a dynamical system change as a parameter varies. It is constructed by plotting the equilibrium values (z) on the vertical axis against the parameter (C) on the horizontal axis.
Conditions: The system is described by a family of ODEs parameterized by C.; Equilibria are determined for a range of C values.
For C=4, the system has only one stable equilibrium. Because there are no other equilibria to act as separatrices, all initial conditions, regardless of their starting value, will converge to this single positive equilibrium as time progresses.
Conditions: The differential equation is dz/dt=4z−z3+4.; C=4 is greater than the bifurcation threshold C* ≈ 3.079.
For C=4, the system has only one stable equilibrium. Because there are no other equilibria to act as separatrices, all initial conditions, regardless of their starting value, will converge to this single positive equilibrium as time progresses.
Conditions: The differential equation is dz/dt=4z−z3+4.; C=4 is greater than the bifurcation threshold C* ≈ 3.079.