What is subcritical Hopf bifurcation?

A Hopf Bifurcation occurs when a periodic solution or limit cycle, surrounding an equilibrium point, arises or goes away as a parameter µ varies. If the limit cycle is unstable and surrounds a stable equilibrium point, then the bifurcation is called a subcritical Hopf bifurcation (cf. [3], p. 264).

What do you mean by the Hopf bifurcation for a two dimensional dynamical system?

Hopf bifurcation occurs when a pair of complex conjugate eigenvalues of the Jacobian matrix of the dynamical system crosses the imaginary axis with a non-zero speed (all the other eigenvalues being in the left half plane) as the control parameter is varied slowly.

What do you mean by Hopf bifurcation?

The term Hopf bifurcation (also sometimes called Poincaré-Andronov-Hopf bifurcation) refers to the local birth or death of a periodic solution (self-excited oscillation) from an equilibrium as a parameter crosses a critical value.

What causes a Hopf bifurcation?

The appearance or the disappearance of a periodic orbit through a local change in the stability properties of a fixed point is known as the Hopf bifurcation. A Hopf bifurcation arises when these two eigenvalues cross the imaginary axis because of a variation of the system parameters.

What is backward bifurcation?

The phenomenon of backward bifurcation in disease transmission models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has been observed in a number of disease transmission models.

What is a bifurcation divorce?

So what is a bifurcated divorce? Simply, they can terminate their marital status and be divorced, whilst setting aside their issues of child custody and access, child support, spousal support and property division for determination at a later date.

What is a bifurcation value?

An equilibrium can become unstable and a periodic solution may appear or a new stable equilibrium may appear making the previous equilibrium unstable. The value of parameter at which these changes occur is known as ”bifurcation value” and the parameter that is varied is known as the ”bifurcation parameter”.

What happens at a bifurcation hearing?

The word bifurcate is synonymous with the words “split” and “divide.” Thus, a bifurcation in a divorce case takes the issue of marital status and splits it from all of the other divorce issues, such as the issues of spousal support, child custody and visitation, child support, and property division.

Can a bifurcated divorce be reversed?

But the court ruled a reversal wasn’t possible. In some states a final divorce decree can be reversed so long as both parties request it and are within the correct time frame. The reasons to reverse a divorce decree include mistake, misfortune, accident or fraud.

What does bifurcation mean in law?

A judicial proceeding that is divided into two stages. The most common division is to determine liabiltiy or guilt in the first stage, and to establish damages or punishment in the second stage.

Which is subcritical Andronov-Hopf bifurcation in the plane?

Figure 2: Subcritical Andronov-Hopf bifurcation in the plane. Andronov-Hopf bifurcation is the birth of a limit cycle from an equilibrium in dynamical systems generated by ODEs, when the equilibrium changes stability via a pair of purely imaginary eigenvalues.

When is the Hopf bifurcation called supercritical or subcritical?

The bifurcation is then called supercritical. If α is positive then there is an unstable limit cycle for λ < 0. The bifurcation is called subcritical. The Hopf bifurcation in the Selkov system (see article).

How does the Andronov-Hopf limit cycle work?

Andronov-Hopf bifurcation is the birth of a limit cycle from an equilibrium in dynamical systems generated by ODEs, when the equilibrium changes stability via a pair of purely imaginary eigenvalues. The bifurcation can be supercritical or subcritical, resulting in stable or unstable…

What do you call an unstable Hopf bifurcation?

The bifurcation is then called supercritical. If α is positive then there is an unstable limit cycle for λ < 0. The bifurcation is called subcritical. The Hopf bifurcation in the Selkov system (see article). As the parameters change, a limit cycle (in blue) appears out of a stable equilibrium.